Class 
Book 




yg±± 



'AtH- 



POPULAR LECTURES 



ON 



inioioiY; ; 



DELIVERED AT THE ROYAL OBSERVATORY OP PARIS. 



BY M. ARAGO, 

MEMBER OF THS INSTITUTE OF FRANCE, ETC. 



EXTENSIVE ADDITIONS AND CORRECTIONS, 



BY DIONYSIUS LARDNER, LL.D. 

FORMERLY PROFESSOR OF ASTRONOMY AND NATURAL PHILOSOPHY IN THB 
UNIVERSITY OF LONDON. 

THIRD EDITION. 



.NEW-YORK: 

GREELEY k McELRATH, TRIBUNE BUILDINGS, 

OPPOSITE THE CITY HALL. 

1848. 



CON T ENTS. 






LECTURE I. 

General Laws of the Reflection of Light. 
General Laws of the Refraction of Light. 



FAGI 

.. 3 
.. 6 



Refracting and Reflecting Telescopes 

Structure of the Eye A 



LECTURE II. 



History of Astronomy 13 

Preliminary Ideas — Definitions 16 

I. Capricornus (Caper) V5 IS 

II. Aquarius ££ ib. 

III. Pisces * ib. 

IV. Aries T ib. 

V. Taurus a ib. 

VI. Gemini LI ib. 

VII. Cancer ZL 19 

VIII. Leoa ib. 

IX. Virgo !TB ib. 

X. Librae ib. 

XI. Scorpio 111 ib. 

XII. Sagittarius t ib. 

LECTURE III. 

Aspect of the Heavens — Apparent Motions of the Hea 
veuly Bodies 19 

LECTURE IV. 



LECTURE VIII. 

Distances, Diameters, Volumes, <fcc, of the Pteuets... 44 

! Kepler's Laws „ _ 45 

' Universal Attraction ,. "\ " 45 

Of the Masses of the Planets 7... .!..'.'. '.'..WW. 47 

LECTURE IX. 

Figure of the Earth 49 

j Dimensions of the Earth 50 

The Earth's Motion 51 

; Diurnal Rotation of the Earth „ ib. 

j Annual Motion of the Earth 53 

LECTURE X. 
Inequalities of the Moon and of the Earth 64 

LECTURE XL 

Comets „ 55 

Halley's and other Comets , .....59 

Physical constitution of Comets 72 



The Fixed Stars 



LECTURE V. 



Distances of the Planets 

The Sun , 

Physical constitution of the Sun.. . 

The Moon 

Physical constitution of the Moon 



LECTURE VI. 

Mercury 9 36 

Physical constitution of Mercury ib. 

Venus $ ib. 

Appearances of Venus as she moves round the Sun 37 

Physical constitution of Venus 37 

Superior Planets : 

Mars i . 38 

Physical constitution of Mars 16. 

The four Telescopic Planets : 

Juno $ 39 

Ceres J 

Pallas O. 

Vssta § 

LECTURE VII. 

Jupiter 2Lj and his satellites 40 

Physical constitution of Jupiter 41 

Saturn > , his Ring and his Satellites 42 

Hcrsehel, or Uranus, 1$, and his Satellites 43 



LECTURE XI F. 



Eclipses of the Moon 
Eclipses of the Sun . . 



LECTURE XIII. 
The Tides 82 

LECTURE XIV. 
Determination of Latitude and Longitude 85 

LECTURE XV 

The Atmosphere 36 

Of the Moon in the Horiron 87 

The Harvest Moon SS 

LECTURE XVI. 

The Seasons and the Days 89 

The Earth's temperature 91 

LECTURE XVII. 

The Calendar 94 

APPENDIX. 

Table of the Constellations, with the Number of Stars 

in each, as far as those of the sixth magnitude .... 96 
Summary ib. 



LC Control Number 




Entered according to Act of Congress, 
BY GREELEY & McELRATH, 
the CUrk'e Office of the Southern District of New-York, in the year 1845 



2004 530040 



ARAGO AND LARIMER'S ASTRONOMY. 



PUBLISHER'S PREFACE. 

To all who are conversant with the existing state of Astronomical Science in Europe, it is well known, that, in 
addition to the regular duties of his office as Royal Astronomer of France, M. Arago has been in the practice of 
delivering each season at the Observatoire, a course of Lectures of a popular kind, which are attended by all classes 
of well informed persons, including ladies in considerable numbers. These discourses are given extemporaneously 
ra the strictest sense of the term, and in style and character, bear a close analogy to those delivered by Dr, Lardner 
in this country within the last few years. It does not appear that M. Arago ever designed their publication, nor that he 
ever even committed them to writing. A person employed by one of the Brussels publishers, reported them, and the 
publication reputed to be M. Arago's Lectures, is nothing more than this report, which, though it could not be legally 
published or circulated in France, obtained through the Belgian booksellers, and their correspondents, an extensive 
illegal circulation in that country. A translation of this report was circulated largely in England. 

The publishers of the present volume, being aware that errors of a more or less important kind, must, under 
such circumstances, have prevailed in the original Belgian edition, and still more in the English translation, and 
that omissions and chasms must have required to be filled up by some person conversant with the science, and capable 
of writing upon it in a clear and familiar style, applied to Dr. Lardner, and induced him to revise the reported 
Lectures, and to add to them such topics as might appear desirable to give them increased utility. The result of this 
arrangement has been the present volume. 

Dr. Lardner desires it to be understood, that he should not have felt himself justified in interpolating any work, 
however elementary, published with the actual sanction of M. Arago's name. But, it being understood, and 
indeed manifested by unequivocal internal evidence, that the Belgian report was unathoriaed and unauthentic, and 
the circulation 0/ some translation of it in this country being rendered inevitable, by the very popularity of its 
reputed author, it was better that a carefully revised copy should be published, than a mere reprint of the En^luh 
translation of the imperfect Belgian report. 

The paragraphs of this volume which are supplied by Dr. Lardner, are distinguished by asterisks. 




,-'?- 



LECTURE I. 

OPTICAL INSTRUMENTS. 



■il'i 



* The 'eye being the organ by which all as- 
tronomical knowledge is acquired, its powers, 
functions and structure, properly form the sub- 
ject of this preliminary lecture, Although the 
natural range of the eye is vast, to a degree al- 
most exceeding belief, yet the researches of 
modern astronomy have demanded a still wider 
scope. The distance of the smallest stars dis- 
tinctly visible to the naked eye is known to be 
such, that light, which moves at the rate of 
nearly two hundred thousand miles per second, 
takes a hundred and twenty years to come 
from them to the earth. The unaided eye, 
therefore, gives us the survey of a sphere around 
us of that scarcely conceivable radius. But this 
is not enough. Art has supplied the telescope 
to extend still more widely the sphere of vision, 
and we can scarcely name any practical limits 
to the powers of this instrument. The largest j 
sad most powerful apparatus of this class, ever 
constructed, was the celebrated forty feet tele- 
scope of Sir William Herschel. By this instru- 



ment, that astronomer was enabled distinctly to 
see individual stars, whose distance is two hun- 
dred times greater than that of the smallest star 
visible to the naked eye. To move over such 
a distance, light would take a period of twenty- 
four thousand years ! The importance of such 
an instrument must be obvious, and those who 
would comprehend the means by which astro- 
nomical science has attained its present state of 
advancement, must feel a corresponding desire 
to study and comprehend it. 

GENERAL LAWS OF THE REFLECTION OF LIGHT 

If we cause a ray of solar light to fall obliquely 
on a polished surface, we mark the following 
resulting 1 nhfinomena: 

1. A part of the light is reflected in a certain 
direction, and if the eye be placed somewhere 
in the line of that direction, it will perceive an 
image of the sun in the line of the reflected ray 
carried backward from the point of reflection . 

2. The poiut where the incident ray meets 



Arago and Lardner's Astronomy. 



the polished surface is visible in every direction ; 
but it appears incomparably less brilliant if seen 
in any other direction than that of the reflected 
ray, the only one which gives a regular image 
of the sun. 

3. A portion of the incident light escapes from 
reflection, and passes through the substance of 
the reflector, if it be transparent, in obedience 
to fixed laws of which we shall speak hereafter. 
If the reflector be opaque, this portion of light 
is absorbed. 

Thus we have before us three very distinct 
phenomena: one portion of the incident light is 
regularly reflected in a special direction ; another 
is reflected indifferently in all directions, and 
disseminated, as if the body on which it falls 
were not polished ; lastly, the remainder passes 
through, or is absorbed by the reflector. 

Now then to investigate the direction followed 
by the portion regularly reflected. We find, 

1. That the incident and the reflected ray lie 
both in one plane perpendicular to the reflecting 
surface. 

2. That the incident and the reflected ray al- 
ways form equal angles with the reflecting sur- 
face; or in other words, that the angle of reflec- 
tion and the angle of incidence are equal. 

Such are the two general laws of reflection, 
from which we shall easily derive an explana- 
tion of the formation of images in this way. 

Let us first take the case of a flat mirror; let S 

Fiff. 1. 




be a radiant point, O the eye of an observer, and 
AB the plane of the reflector. Among all the 
luminous rays issuing from S there will be one, 
SI for instance, which, after having been re- 
flected from the mirror, will go and meet the eye 
at O, taking the direction 10, and thus making 
the angle of incidence equal to that of reflection. 
From the radiant point S, let us draw SA per- 
pendicular to the reflecting surface, and produce 
this line on the other side of the mirror, so that 
AD may be equal to SA; then, from the point 
D let us draw the line DO to the eye ; DO will 
be the direction of the reflected ray, and the 
point I, where it cuts the surface of the mirror, 
will be the point of incidence. Moreover, if 
the luminous object and the eye be supposed to 
be mathematical points without sensible dimen- 
sions, the ray determined in the preceding man- 
ner is the only one that can be reflected toward 
the eye. 

But the opening of the pupil, which admits 
the rays of light, is not a mathematical point ; it 



is a space, the diameter of which in man is 
about 2-25ths of an inch, and which we may 
represent by LL. All the reflected rays then 

Fig. 2. 




that find entrance through this opening, will 
arrive at the retina, and contribute to vision. 
Now, each of these rays may be determined by 
the same construction that we have just em- 
ployed, whence it is evident that they will form 
a cone with a circular base, the vertex of 
which is at D, and the base at LL. It is a known 
fact that the eye, when it can judge of the 
distance of luminous points, always supposes 
them situated in the point from whence the rays 
that fall upon the eye seem to diverge.* Thus 
the eye being placed at 0, the luminous point 
will appear to it, when seen by reflection, to be 
situated at D, that is to say, as far behind the 
mirror as it is actually before it. 

If the luminous object be of a certain extent, 
each of its radiant points will form its own sepa- 
rate image, in accordance with the laws we 
have just explained, and these images taken to- 
gether, will form that of the object. Let us 
suppose for instance that the object is an arrow 

Fig. 3. 




* See also Lecture XV. 






Arago and Lardner's Astronomy. 



SS' ; the butt S of the arrow will form its image 
at D, the point S' will form its own at D', and 
the intermediate points will present theirs along 
the line DD'. Thus the whole image will be 
comprised between the extreme reflected sets 
ok pencils of rays DO and D'O ; its absolute size 
DD' will be equal to SS', that is to say, to that 
of the object itself, but it will appear inverted 
from right to left. 

These observations are sufficient for the solu- 
tion of all questions that can possibly arise with 
respect to the reflection of light, and to vision 
of objects by means of plane mirrors. 

As for curved surfaces, of whatever form, to 
determine generally the apparent place, the 
form and the size of the images they reflect, it 
is enough to consider the reflection of each lu 
minous ray, as if taking place upon the plane 
tangent to the curved surface at the point of in- 
cidence. But for practical purposes, it is not 
necessary to apply this reasoning to all kinds 
of curves, for we never make use of any other 
than spherical reflectors, whether concave or 
convex, these being the only ones that can be 
shaped and polished with accuracy; and to ob- 
tain precise images even from these, it is neces- 
sary that the luminous rays should fall almost 
perpendicularly on their surfaces. We shall 
therefore confine ourselves to the examination 
of this single case. 

Let us suppose then in space, a luminous 
point casting its rays on the several parts of a 
spherical surface, concave or convex, and con- 
fining our observations to one of them, let us 
investigate the direction *in»which it will be 
reflected. 

Let MAM' be the spherical mirror, S the lu- 

Fie. 4. 




minous point, and SI the incident ray we are 
considering. From the point I to the centre of 
the sphere draw the radius IC, and lay down 
the angle CIR equal to CIS: IR will be the di- 
rection of the reflected ray. 

If we repeat the same construction for all the 
incident rays issuing from S, we shall find by 
our figure, as well as by calculation, that the 
reflected rays all pass very close to each other 
through a small space called the focus, forming 
here by their concentration an image of the 
point S: and this is also confirmed by expe- 
rience. 

By a similar construction and mode of rea- 
soning, we should find that the image formed 
by a convex mirror is always imaginary, and 
takes place beyond the mirror, so that it can 
only be seen by the naked eye, but not received 
on a roughed glass or on a screen 

* The image of an object formed by a reflector, 




Fig. 5. 



iie 



differs in its position from the object itself, ac 
cording to the form of the reflector. 

* In plane mirrors, the image is laterally but 
not vertically inverted. That is to say, the right 
hand of a person looking into a mirror, corres- 
ponds with the left hand of the image. When 
an image is formed by a concave mirror, it is in 
verted, both laterally and vertically, that is say, 
right becomes left, and left right, and the image 
is also turned upside down. 

* When an object is presented to a convex 
mirror, the image is always vertically erect, but, 
as in the plane mirror, it is laterally inverted. 

Illustration. Let AB 
represent a plane mirror, 
and EF any object, as an 
arrow ; then draw from the 
points E and F, the per* 
pendiculars EG and FH to 
the surface of the mirror, 
and produce those lines to 
V e and /, so that EG shall be 
A equal to eG, and FH to /H, 
\ and ef will be the position 
~~'h?e °f the image which will be 
_Sf'' exactly equal to the object, 
as the quadrilateral fig- 
ure Ge/H will be equal 
to the quadrilateral GEFH. From inspection of 
this figure it will be perceived, that the rays of 
light proceeding from that part of the object 
nearest to the surface of the mirror, will be re- 
flected so as to form the part of the image near- 
est to the plane of the mirror in the opposite 
direction. Hence, when trees or buildings, or 
any other objects, are reflected from a horizontal 
plane, as the surface of a pond, or a smooth 
stream of water, they will appear inverted ; for 
their lower parts being nearest to the reflecting 
surface, are seen immediately within it, while 
their tops seem to hang downward or to extend 
deeper beyond the surface. 

When a mirror, C, 
Fig. 6. in the following figure, 

is inclined forward at an 
^s. angle of 45 deg., an ob- 
f b ject AB, if placed in a 
vertical position, will 
form a horizontal image 
ab; and if the position 
of the object be horizon- 
tal, that of the image 
will be inverted. — [See 
Gale's Natural Philoso- 
phy. 

The following properties of concave mirrors, 
are extracted from the same work : 

The focus of a concave mirror is the point 
in which the reflected rays meet. The centre 
of concavity is the centre of the sphere, of which 
the mirror forms a part. Parallel rays, falling on 
a concave mirror, are converged to a focus half 
way between the centre of concavity, and the 
surface of the mirror. 

Parallel rays reflected from a concave sur- 
face, are made converging. 

Illustration. The parallel rays 1, 2, 3, 4, &c, 
fig. 7, are converged by reflection from the 
concave mirror, and meet in the focus o, half 
way between the centre a, and the surface of 
the mirror. 




Arago and Lardner's Astronor. 



iff. 



Fig. 7. 



\ 




GENERAL LAWS OF THE REFRACTION OF LIGHT. 

We have just seen how that portion of the 
luminous ray conducts itself, which is reflected 
from the surface of bodies ; we shall now follow 
that portion which traverses their substance. 

The latter, when the incidence is oblique, 
does not continue in the straight line — it devi- 
ates from its course; this is the phenomenon 
called the refraction of light. 

* When a ray of light meets the surface of a 
transparent medium, such as water or glass, in 
a line perpendicular to that surface, it will pass 
through without changing its course; but, if it 
meet the surface at any oblique angle, it will be 
bent into another direction, which will depend 
on the direction of the incident ray, and the re- 
lative densities of the media, between which 
the ray passes. Generally, when it passes from 
a less dense into a more dense medium, it is 
bent toward the perpendicular drawn to the 
surface of the medium at the point of incidence of 
the ray. In this deflection it does not leave the 
plane passing through the incident ray, and that 
perpendicular. 

* This is the case with all uncrystallized trans- 
parent substances ; but, in the case of certain 
transparent crystals, the phenomena are niucb\ 
more complicated, involving the consideration 
of the laws of polarization. Since, however, 
these have no necessary connection with the 
main subject of this treatise, we shall not enter 
here into any exposition of them. 

The following illustrations of refraction are 
taken from the work above quoted : 

Rays of bght are always refracted toward a 
perpendicular to the surface in entering a denser 
medium ; and this refraction is, more or less, in 
proportion as the rays fall more or less obliquely 
on the refracting surface. 

Illustration 1. Let cd, fig. 8, represent a 
thick plate of glass, or a 
vessel of water, and ao, 
a ray of light refracted 
at o, and entering the 
denser medium, so that 
instead of continuing in 
the direct line, it moves 
in the direction on ; but 
when it passes out of 
this medium into air at 
n, it is again bent away 
from the perpendicu- 
lar to the medium, and 
moves in a direction 
parallel to ao. 



Fig. 8 




2. Refraction of water may be shown in 
another way: Prepare a blackened vessel, and 
place it in such a position that the spectator, in 
a given place, cannot see the bottom; now pour 
in a few globules of quicksilver, or place a 
bright silver coin on the bottom; this will not fee 
seen by the spectator, but by filling the vessel 
with water, the metal on the bottom will be 
distinctly seen from the refracting power of the 
water. The truth of the remarks above will be 
verified by inspecting fig. 9, where the eye 
could not see the metal c, while the vessel was 
empty, except by raising it to the position b; but 
on filling the vessel with water, the object by 
refraction is raised to a, where the rays pro- 
ceeding from it reach the eye of the observer. 
Objects seen obliquely in water appear elevated. 




When light passes out of a denser into a 
rarer medium, btmfcves in a direction farther 
from the perpendicular. 

Illustration 1. It will be perceived by tra 
cing the line indicating the ray of light proceed 
ing from the metal in fig. 9, that when it pas 
ses from the water into the atmosphere, it 
bends away from a line perpendicular to the 
surface o.f the water. 

2. Take »a glass goblet half filled with water, 
"teM^put a^half dollar into it, and invert over it a 

small plate or saucer. The bystander will sup- 
pose that he sees two pieces, the-one -a -half dol- 
lar, and the other a dollar — the firs-t'is»seen by 
the rays refracted from the surface of the water, 
and the second from refraction through the side 
and through the rounded side of the goblet. 

3. Another example of refraction may be 
seen, by putting a staff obliquely in the water, 
and observing that it always appears as if bent 
at the surface of the liquid. In like manner 
by observing the sandy bottoms of rivers, objects 
on the bottom appear more elevated than they 
really are, from the refraction of the rays of 

4. Rays which pass perpendicularly from one 
medium to another, suffer no refraction. 

The next thing to be determined is, the rela 
tion existing for every degree of incidence be- 
tween the obliquity of the incident ray to the 
perpendicular, and that of the refracted ray ; so 
that, one of these directions being given, the 
other may be calculated ; and here we are 
aided by the two following laws. 

1. The incident ray and the refracted ray 
are always in one plane, -perpendicular to the 
common surface of the two media. 

2. The ratio of the sine of the angle of re- 



Arago and Lardner's Astronomy. 



fraction to the sine of the angle of incidence, is 
always the same for the same medium, whatever be 
the angle of incidence. This is what is called 
the ratio of refraction. 

The act of refraction is always accompanied 
by & remarkable phenomenon. The refracted 
rav is decomposed into rays of different colors, 
the refrangibility of which increases from the 
red ray, where it is least, to the violet ray, 
where it attains its maximum. This is the phe- 
nomenon of the disjjersion of light. 

Besides the seven prismatic colors, experi- 
ments have also detected in the refracted ray, 
rays of caloric, the intensity of which augments 
from the violet ray up to and beyond the red, 
and chemical rays, the intensity of which fol- 
lows a diametrically opposite course ; that is, it is 
at its minimum in the red ray, and its maximum 
lies beyond the violet. 

* It may appear difficult of comprehension to 
say that there are rays of light which are not lu- 
minous, which is equivalent to stating that these 
rays are not light. Nevertheless when properly 
explained, there is no difficulty in comprehend- 
ing this. It was shown by Newton, that a glass 
prism has the power of subdividing a ray of solar 
light into a great number of component rays, 
and that these component rays differ from one 
another in several particulars. Thus, they are 
refracted, in different degrees, by any transpa- 
rent medium through which they may pass ; 
they differ in color ; they differ in their degree 
of brightness ; they differ in their heating pow- 
er ; they differ in the effects they produce on 
certain chemical preparations, such as the chlo- 
ride of silver. But we also find that rays issue 
from the prism, which affect the thermome- 
ter, and others which affect the chloride of sil- 
ver, and which are not visible. The existence 
of such rays is detected by their effects, not on 
the eye, but on the thermometer and the chem- 
ical preparation we have just named ; and 
what is still more remarkable, they produce 
their respective effects with more energy than 
any of the visible rays ; that is to say, we find 
invisible rays which will raise the thermometer 
higher, and others which will affect the chlo- 
ride of silver more actively than any of the visi- 
ble colored rays of the prismatic spectrum. 

The discovery of the compound nature of 
light, was made by Sir Isaac Newton, in the 
following manner : 

Illustration 1. Let a bundle of rays proceed- 
ing from the sun S, be admitted through the 
window shutter of a darkened room as repre- 

Fig 10. 




sented in the figure below, and allowed to fall 
on the ti-iangular piece of glass ABC, called 
the prism. A ray D thus entering, and suf- 
fered to pass unobstructed, would form on a 
plane surface a circular disk of white light E, 
but the prism being so placed that the ray may 
enter and quit it at equal angles, it will be re- 
fracted in such a manner, as to form on a screen 
MN, properly placed, an oblong image called 
the solar spectrum, and divided horizontally 
into seven colored spaces, or bands of unequal 
extent, succeeding each other in the order rep- 
resented : red, orange, yellow, green, blue, indi- 
go, violet. 

2. These bands are not separated by dis- 
tinct lines, so that it is difficult to determine 
where one ends and another commences ; the 
several tints at their borders being blended, 
and each almost imperceptibly united with 
those next to it ; the whole spectrum exhibiting 
the seven principal colors, with intermediate 
shades or mixtures. 

Observation 1. It will be seen by the forego- 
ing figure that all the rays are somewhat bent 
out of their course, the violet the most, and the 
red the least. 

2. The rectangular screen MN, on which is 
received the different rays, is called the spec- 
trum. 

Experiment 1. The following experiment is 
often cited as evidence of there being seven 
primary colors, namely, that if the different 
prismatic colored rays be allowed to pass 
through a double convex lens, they become 
white-light. 

2. The same effect is produced by mixing 
in the proper proportions seven different colored 
powders ; or still better, by painting the seven 
colors on a circular board, in the proportions 
occupied by these several colors in the spec- 
trum, and whirling the board very rapidly. 



When a ray of light is received on a glass 
prism, it is refracted and approaches the base of 
the prism, in conformity with the laws we have 
just expounded. Now we may conceive a sys- 
tem, a combination of prisms, shaped and ar- 
ranged in such a manner that the rays refracted 
by them shall converge to the same point. We 
can very readily imagine how desirable it would 
be, to be thus able to concentrate in one point, 
a great number of rays of light ; but the diffi- 
culty of constructing such an apparatus with 
sufficient accuracy would have greatly hindered 
the progress of science, if by rare good fortune 
it had not happened to be 
ready constructed in spheri- 
cal lenses, which are nothing 
else than a combination of 
prisms, and which may be 
executed with accuracy and 
facility. 

* Lenses are of six spe- 
cies : 

1. The double convex lens 
is one bounded by spherical 
surfaces, the concavities of 
whicli are presented toward 
each other. Fig. 11, a. 

2. The plano-convex lens 



Arago and Lardner's Astronomy. 




Fig. 11, a is one bounded by a plane and 
a spherical surface, the concav- 
ity of the latter being turned 
toward the former. Fig. 11, b. 

3. The meniscus, is a lens 
bounded by two spherical sur- 
faces, the convexity of one be- 
ing presented to the concavity of 
the other, and the radius of the 
latter being less than the radius 
of the former. Fig. 11, c. 

4. The concavo-convex lens, 
is similar to the meniscus, ex- 
cepting that the radius of the 
concave surface is less than the 
radius of the convex surface. 

5. The plano-concave lens, is 
one bounded by a plane and a 
spherical surface, the convexity 
of the latter being turned to- 
ward the former. Fig. 11, d. 

6. The double concave lens, 
is one bounded by spherical sur- 
j faces, the convexities of which 

Hjare turned toward each other. 
Fig. 11, e. 

In their general optical cha- 
racter, the plano-convex lens, and the meniscus, 
are similar to the double convex, and the pla- 
no-concave, and concavo-convex, are similar to 
the double concave. 

These forms may be divided into classes, ac- 
cording as the bases or the points of the con- 
stituent prisms are turned toward the axis of 
the lens ; and as refraction always takes place 
toward the base of the prism, the former will 
cause the rays of light which fall in a parallel 
direction on their surface, to converge — the lat- 
ter, to diverge : hence they are called, respec- 
tively, converging and diverging lenses. 

We know how these different classes of lenses 
are made to assist vision, in correcting the too 
"weak convergence of the rays on the eyes of 
long-sighted persons, and its too rapid conver- 
gence in the short-sighted. But it does not 
concern our present purpose to dwell on this. 

Let us cause a pencil of parallel rays to fall 
on a convex lens, and examine the result more 
closely. 

Among the incident rays ; 
Fig. 12. there is one that coincides 

with the axis of the lens, aud 
SSSSSSSSS traverses it without being re- 
fracted; but this is not the 
case with the others, which 
undergo a refraction, the 
greater in proportion as they 
are further removed from the 
axis, so that they all converge 
toward the same point F. 
This point is called the focus 
jf the lens. We perceive 
that the greater the convexi- 
ty of the lens, the greater 
will be the refraction, and 
consequently the shorter the 
distance of the focus. 
Reciprocally, if having arrived at the focus F, 
the rays of light now retrace their course, they 
will be refracted by the lens, and will escape 
from it all parallel ; whence follows this re- [ 




markable inference ; that if from the focus of a 
lens, rays of light be directed upon every part 
of its surface, they will form on issuing from it a 
parallel pencil. 

This property of lenses has given birth to an 
extremely useful contrivance : the light-house 
lamp is nothing more than a combination of 
four lenses, in the common focus of which a 
lamp is placed, the rays escaping from which 
arrange themselves in parallel pencils on issu- 
ing from the lenses, and no longer weakened 
by dispersing, lose nothing of their intensity, 
except what is absorbed by the imperfect trans- 
parency of the atmosphere, so that they can il- 
luminate the most distant portions of the hori- 
zon. But as the diame;er of these luminous 
pencils is necessarily circumscribed, and as in 
spite of the eccentricity of the lamp, its light 
can irradiate only a part of the horizon at a 
time, the expedient has been devised, in order 
to direct the light upon every point of the hori- 
zon successively, of making the light-house re- 
volve on its centre in a given time, which, vary 
ing for each light-house, serves to distinguish 
them all from each other. Thus this useful ap- 
paratus not only warns the mariner of his ap- 
proach to the coast, but moreover indicates to 
him his position by its mode of rotation. 

Another property of lenses is that of enlarging 
the images of objects. Let us remember that 
the apparent dimensions of a body depend on 
the angle under which it is seen, and that this 
angle varies inversely, as the distance of the ob- 
ject from the eye of the observer. Whence it 
follows, that to see an object under large di- 
mensions, we should only have to place it close 
to the eye, if vision could take place thus with 
distinctness ; but the great divergence of the 
rays in this case renders the image confused. 
To avoid this, let us look at the object through 
a converging lens. The parallelism of the rays 
will allow of the eye to approach it as much as 
we please, and the image of the object will ap- 
pear under an angle, equal to that under which 
the object itself would be seen by the naked 
eye, if direct vision could possibly take place at 
so short a distance. Hence we perceive that 
the magnifying power of a lens is the greater, 
the less its focal distance. 

In the experiment we have just mentioned, 
the idea we form of the real size of an object, is 
determined by the angle under which it is seen, 
without our being able to modify it by any pre- 
vious experience of the relation between dis- 
tances and visual angles. This is not the case 
in the ordinary process of vision. Two things 
enter into the judgment we form of the size of 
objects — the angle under which we see them, 
and the distance at which we suppose them to 
be. Thus we judge very well of the height of 
two 'men placed at unequal distances from us, 
and consequently seen under different angles, 
because we make allowance for the distance. 
So true is this, that this invariable habit of al- 
lowing rigidly for distance, leads us into error 
as to the real dimensions of the body when we 
are mistaken as to the distance. Thus objects 
seen through an opera-glass do not appear mag- 
nified, because we think them nearer ; and yet 
such glasses magnify two or three times, as we 
may convince ourselves by looking with one 



Arago and Lardner's Astronomy. 



eye through the opera-glass, with the other na- 
ked. Here is another experiment: place an 
object on a horizontal plane, and place your 
eye in the continuation of the same plane ; then 
look at the object, while you push your lower 
eyelid slightly with your finger, so as to see 
two images ; that which is nearer to you will 
appear to diminish in proportion as it approach- 
es you more. The proof that this opinion as to 
the respective size of the images depends on 
the supposed distance is, that they will appear 
to you equal when you shall have placed the 
object on a vertical plaue, so as to obtain the 
two images one above the other. 

To return to our lenses. We have seen un- 
der what laws a pencil of parallel rays is re- 
fracted ; let us see how rays issuing from the 
dilferent points of an object are refracted. Let 
AB be an illuminated object. It is evident that 
from each point of this object will issue a pen- 
cil of rays, whose point of convergence will be 
found somewhere in the prolongation of that 
which, having encountered 
two parallel faces, has not 
undergone any refraction. 
Thus the point A will be 
imaged at A' ; the point B 
at B' and the intermediate 
points along the line con- 
necting A' and B'; and if 
these rays be received on a 
sheet of paper or of ground 
glass, we shall see a rever- 
sed image of the object AB. 
We have already remark- 
ed, that a refracted ray of 
eolar light is decomposed 
into rays of different colors. 
This decomposition colors 
the image and renders it con- 
fused. So great is the incon- 
venience resulting thence, 
that Newton, knowing no 
remedy for it, regarded it as decisive of the un- 
fitness of refracting telescopes for astronomical 



ray of the pencil, 



13. 




purposes. But since his time, means have happi- 
ly been found for remedying this defect. This 
consists in combining together lenses formed of 
substances which, though they equally refract 
light, yet disperse it unequally. Crown glass 
and flint glass fulfil these conditions, and it is 
by combining these two kinds of glass in the 
proper proportions, that we have succeeded in 
obtaining the achromatic object-glasses employ- 
ed in the present day. 

REFRACTING AND REFLECTING TELESCOPES. 

Astronomical refracting telescopes may be re- 
garded as consisting essentially of two glasses : 
the one named the object-glass, receives the 
rays proceeding from the object and forms an 
image of it in its focus ; the other, the eye-glass, 
serves for looking at this image. The enlarge- 
ment produced by this kind of telescope, pro- 
ceeds from two causes : when seen by the na- 
ked eye, because it is at a distance of but seven 
or eight inches from it, a distance much less 
than that which separates the lens from the fo- 
cus, so that it is thus seen under an enlarged 
angle; but its enlargement is particularly due 
to the eye-glass, which is a lens of very short 



focal distance. Astronomical refracting tele- 
scopes are very powerful ; some of them magnify 
as much as a thousand of times. 

Reflecting telescopes consist of a polished 
metallic reflector, in the focus of which the im- 
age is formed by reflection ; but as this image 
cannot be seen through the reflector, a small 
mirror is employed to project it laterally, or else 
behind the reflector through a small opening 
made in it for the purpose. This double reflec- 
tion is attended with the inconvenience of con- 
siderably diminishing the light, for it is well 
known that the most polished mirror hardly re- 
flects more than half the light incident upon it. 
Thus with equal dimensions, a reflecting tele- 
scope has only a fourth part of the power of a 
refracting telescope, for refraction does not sen- 
sibly diminish the light. 

, To measure the height of the stars, and for a 
multitude of other operations, refracting tele- 
scopes have in their field of view metallic 
threads variously arranged, and of extreme del- 
icacy, since they are considerably finer than the 
filaments of spiders' webs. The means by which 
they are procured is ingenious : these threads, 
which are of platinum, are first drawn out as- 
fine as they can be made with the wire-draw- 
ing apparatus. They are then put into cylinders, 
into which melted silver is poured, and thus 
they form the axis of silver cylinders, which are 
themselves subjected to the wire-drawing pro- 
cess. The platinum being thus further reduced 
in dimensions, to free it from the silver, the 
whole is plunged in nitric acid, which dissolves 
the silver without acting on the platinum. 

* A telescope is in fact a device by which a 
small image or picture of a distant object is 
formed, so that it can be viewed by the eye at 
a very short distance. This image is then exam- 
ined by a microscope, by which it can be magni- 
fied within certain limits depending on the mag- 
nitude of such image, and the precision with 
which it is formed. To understand this, it 
must be remembered, that the object-glass of 
the telescope is a convex lens, in the focus of 
which will be formed an image of any distant 
object to which the tube of the telescope is di- 
rected. The focus where this image is placed 
is in the tube of the telescope, very near to the 
extremity, to which the eye is applied. The 
eye-glass inserted at that extremity, is in fact 
nothing but a microscope by which the image 
in the tube is examined, exactly as any minute 
object is viewed by a common microscope. It 
appears then that when we look through a tel- 
escope at an object, it is not the object itself 
that we see, any more than it is our own per- 
son itself that we see when we look in a mir- 
ror. It is an image of the object magnified by 
a microscope. We could in fact see that image 
without the eye-glass, but that the structure of 
the eye does not admit of our viewing it suf- 
ficiently closely. 

* The only difference between the case of a 
refracting telescope, such as we have now de- 
scribed, and a reflecting telescope is, that the 
image in the latter is formed by a spherical re- 
flecting speculum, usually made of finely pol- 
ished metal. But the application and use of 
the eye-glass is the same in both. 

* These observations on telescopes will be 



10 



Arago and Lardners Astronomy. 



further elucidated by the following diagrams, 
and illustrations from Gale's Natural Philo ophy. 

Telescopes are instruments for viewing dis- 
tant objects, and are of two kinds, Refracting 
and Reflecting. 

In the first kind the image of the object is 
seen with the eye directed toward it, and in 
the second, the image is seen reflected from a 
mirror 



The most simple refracting telescope consists 
essentially of two convex lenses, one toward 
the object and called the object-glass, the other 
j next the eye called the eye-glass. The distance 
J of the lenses from each other must be such that 
their foci will meet in the same point ; or in 
other words, the distance must be equal to the 
sum of their focal distances. 

Illustration. See the wood cut below. 



Fig. 14 




The above figure represents the glasses of I 
the telescope without the tube, which, though 
generally used, is not a necessary appendage to 
the instrument. 

To explain further the principles of the tele- 
scope ; let the focus of the object-glass a, in the 
last figure, be 8 inches, and that of the eye- 
glass b, be 2, then the sums of their foci will be 
10 inches; therefore the two lenses must be 
placed 10 inches apart. 

To illustrate this subject still further, let cd, 
&c, represent the rays from some distant object, 
as the moon, then the image formed by the ob- 
iect-glass a, and seen through the eye-glass b, 



will have its apparent diameter very much 
magnified. 

With such a telescope the image will, with 
respect to the object, be inverted, but in view- 
ing celestial objects, this circumstance is a mat- 
ter of no consequence. 

The Terrestrial telescope is used to view ob- 
jects on the earth in an erect position, and con- 
sists of an object-glass, and three eye-glasses. 

Illustration. The manner in which the ob- 
ject is made to appear erect, and in which the 
rays are brought to a focus, may be learned 
from the figure below. 



Fig. 15. 




The diagram, fig. 15, represents the terres- 
trial telescope, consisting of an object-glass and 
three eye-glasses, as a, b, c, & d — the object of 
the two additional eye-glasses is to cause the 
object to appear erect, but they do not alter its 
apparent diameter. All the glasses are placed 
at the sum of their focal distances from each 
other, as may be seen by inspecting the figure, 
and the course of the rays may also be seen, by 
tracing the lines in the diagram, where o repre- 
sents the object, and the rays coming from it 
are refracted by the lens a, and converged to a 
focus at/, where they cross each other, and pass- 
ing through the lens b, are rendered paral- 
lel ; passing through c, they again cross each 
other, as seen by the lines of the diagram and 
the position of the arrow; and by passing 
through the lens d, are rendered more nearly 
parallel, in which state they enter the eye, on 
the retina of which the image is painted in- 
verted, but making the object appear erect. 

Observation The common spy-glass is an 
instrument of this kind. Those of the best 
manufacture, will enable one to see distinctly 
the satellites of Jupiter, and will for most pur- 
poses answer as a substitute for the telescope. 



To ascertain the comparative value of a tele- 
scope, place a paragraph of a newspaper or 
other fine print, and measure the distance re- 
quired to read it, by the instrument to be tried, 
and compare with a standard instrument. 

The magnifying power of the reflecting tele- 
scope is found by dividing the focal distance of 
the object-glass by the focal distance of one of 
the eye-glasses. 

The common reflecting telescope consists of 
two reflectors, and one or more convex eye- 
glasses. 

Illustration. The following diagram shows 
the general construction and effect of the New- 
tonian reflecting telescope, in which the concave 
metallic speculum CD receives the rays issuing 
I from the object AB, which it renders conver- 
j gent, and thus forms a reversed image in the 
i plane mirror EF, inclined at an angle of 45 de- 
grees ; and this image being reflected to dc, at 
the focus of the lens or eye-glass GH, is seen 
through the aperture before it by the observer. 

Observation. In the original, or Gregorian 
telescope, the image is viewed by looking 
toward the object, as in the refracting tele- 
scope ; and there are other modifications of this 



Arago and Lardner's Astronomy. 



Fig. 16. 




instrument, as those of Cassegrain and Herschel, 
which need not be introduced in so short and 
general a treatise, as the present work is in- 
tended to be. 

* These two species of telescopes, have each 
its peculiar advantages and defects. Whether 
the surface on which light strikes, be one which 
reflects or refracts, a portion of this incident 
light will be lost, and the remainder alone pro- 
ceeds to form the image. But this loss is much 
greater in reflection than in refraction. A re- 
fracting telescope will therefore afford a more 
strongly illuminated image than a reflecting tele- 
scope of equal magnitude. In reflection, rays 
of light of all colors are turned in the same di- 
rection, but in refraction, rays of each different 
color follow a different direction, and are brought 
to a different focus. This produced a defect in 
refracting telescopes, which, lor a long time, 
gave the superiority to reflecting instruments. 
But this imperfection was removed by the 
expedient referred to by M. Arago, by which 
the refracting telescope was rendered achro- 
matic. 

* Whether the telescope, however, be a re- 
flector or refractor, the brightness, and therefore 
the distinctness, (so far as distinctness depends 
on illumination) of the image, depends, ceteris 
paribus, on the magnitude of the speculum in 
the one, and of the object lens in the other. 
The entire extent of each of these is employed 
in forming each point of the image, and the 
larger they are, the more rays combine in illu- 
minating each point. Hitherto obstacles almost 
insurmountable, have prevented the construc- 
tion of very large object lenses for refracting 
telescopes. Thus, a lens much above twelve 
inches diameter, has probably never been pro- 
duced fit for such an instrument. On the other 
hand, there is scarcely any practical limit to the 
magnitude of the specula of reflecting tele- 
scopes. Notwithstanding therefore the greater 
loss of light by reflection, more powerful illumi- 
nation has been obtained by reflecting than by re- 
fracting telescopes. The great telescope which 
obtained such celebrity in the hands of Sir Wil- 
liam Herschel, showed the star Sirius with such 
splendor that the observer was obliged, in view- 
ing it, to protect his eye by a colored glass. 

STRUCTURE OF THE EYE. 

We shall conclude this first lecture with an 
account of the organ of vision, the most won- 
derful of all optical instruments. In man, this 
organ is formed of different transparent media, 
the curvatures and refractive forces of which 
are so combined as to correct the aberrations of; 
sphericity and refraction. The images are form- 1 
ed on a nervous membrane, coating the inner ; 




part of the eye, which transmits 
to the brain the impression it re- 
ceives. 

This organ is composed of three 
transparent media, differing in 
form and in refractive power. 
The first is a meniscus, filled 
with a transparent liquid, similar 
in appearance to water, and hence 
called the aqueous humor. Next 
comes a solid transparent body in 
the form of a double convex lens, 
and called the crystalline lens, pHp. It is less 
convex anteriorly than posteriorly, and its flat- 
ness increases with age. Finally, the whole of 
the posterior chamber is occupied with a viscid 
fluid, like melted 
Fig. 17. glass, and therefore 

called the vitreous 
humor. The mem- 
branes enveloping 
this whole appara- 
tus, may be regard- 
ed as prolongations 
of the integuments 
of the optic nerve. 
The exterior integ- 
ument of the nerve 
gives origin to the 
outer coat of the 
eye, which is tough, opaque, but yet flexible, 
somewhat like horn, and is called for this rea- 
son, the sclerotic or the opaque cornea, ABCD 
But arriving in front of the eye, this membrane 
becomes thinner and transparent, like a watch- 
glass, in order to give passage to the light ; it 
then takes the name of the transparent cornea, 
A ED. Here it is covered by the skin, which 
in this place is of extreme thinness. The sec- 
ond envelope of the optic nerve expands be- 
neath the former, and forms a coat called the 
choroid, which is covered with a black pigment ; 
for just as we blacken the interior of the tubes 
of our telescopes, it is necessary that the inte- 
rior of the eye too should be blackened, to pre- 
vent the confusion which would otherwise have 
resulted from the multiplied reflection of the 
rays. Lastly, the interior medullary portion of 
the optic nerve, expanding in its turn like the 
former, forms a nervous membrane of a grayish 
color, resting on the choroid, and denominated 
the retina. It is presumed to be the seat of vision. 
It is now easy to understand in what way 
vision is effected. The rays issuing from exter- 
nal objects fall on the cornea, traverse the 
aqueous humor, the crystalline, and the vitre- 
ous humor, and concentrate themselves on the 
retina in the focus of the instrument, where 
they form a small reversed image. This cau be 
seen in the eyes of men or animals extracted 
shortly after death. If we carefully pare away 
the upper part of the sclerotic, and place a 
strongly illuminated object in front of the eye at 
a convenient distance, we shall see, on looking 
backwards, a very exact image of the object 
formed at the bottom of the eye, varying in size 
inversely with the distance. 

In optical instruments exact and distinct ima- 
ges cannot be procured of objects at unequal 
distances, unless by means of proportionally 
varying the focal lengths of the instrument. By 



12 



Arago and Lardner's Astronomy. 



what mechanism is this condition fulfilled in the 
eye, in which vision is effected with equal dis- 
tinctness at very various distances? For that 
something takes place in the eye analogous to 
the variations of the focal lengths of the instru- 
ment, is proved by the fact, that the eye re- 
quires a certain time, and even the exertion of 
a certain effort, thus to vary its range : of this 
we may satisfy ourselves by placing a small ob- 
ject, as for instance a hair, at a short distance 
from the eye, so that it may be projected on an- 
other more distant object : it will be impossible 
for us to see both objects distinctly at once, but 
the eye will be forced to pass alternately from 
one to the other. Anatomy, however, has vain- 
ly endeavored to discover by what mechanism 
the organ is enabled thus to vary its effects. It 
was at first supposed that the anterior part of 
the cornea was capable of voluntarily assuming 
a more or less convex form, or else that the re- 
tina had the power of advancing or retiring a 
little to meet the shifting positions of the focus, 
but accurate experiments have proved the falla- 
cy of these two hypotheses. There remains 
then the crystalline lens to effect the phenome- 
non in question ; and it appears probable, al- 
though the opinion does not seem countenanced 
by anatomy, that it is to the crystalline lens the 
eye owes its power of seeing distinctly at vari- 
ous distances ; for with the loss of the crystalline 
lens the eye loses this faculty. Thus persons 
who have been operated on for cataract — that is, 
who have had the crystalline lens destroyed 
when it had lost its transparency — do not see 
well but at a certain distance, and that gener- 
ally a long one. 

But how is it this act of vision gives rise to sen- 
sation ? We cannot tell ; all we know is, that 
the impression produced on the retina is trans- 
mitted to the brain by the optic nerve. Rea- 
soning from this fact, Mariotte supposed that the 
more the image approached the point from 
whence the nerve begins to expand into the re- 
tina, the more acute would be the sensation, 
and that it would reach its utmost intensity 
when it was formed exactly over that point. 
Experiment presented him with a diametrically 
opposite result ; for he recognized, by means of 
a very simple process, that this point of the re- 
tina is insensible, and that an object becomes 
invisible as soon as it is so placed that its image 
may fall on this spot. 

The axis of the eye — that is, the direction in 
which we habitually look — is not that in which 
we see objects best. This is the reason why 
astronomers say, that to see a star one should not 
look at it ; that is to say, that one sees it better 
by looking at the part of the heavens near that 
which it occupies. 

The sensation produced on the retina by the 
rays of light is of some duration ; this is the rea- 
son why a live coal, swung rapidly round, ap- 
pears a luminous hoop : and if one were to make 
it turn behind an opaque screen with a hole in it, 
so that the coal could only be seen as it passed 
the hole, it would appear there continually, if 
the motion were sufficiently rapid that it should 
present itself ten times in a second. 

When we look for a long while on one color, 
it produces a morbid sensation in the fibres of 
the retina, unfitting it for some time to perceive 



that color, and making its complementary color 
predominate. Thus, after having looked for 
some time on red or green, we see green or red 
spots on the objects we turn our eyes upon ; be- 
cause these two colors are complementary the 
one of the other; that is to say, mixed together, 
they produce white. 

It is probable the fibres which perceive one 
color are not those that perceive another. Such 
at least appears the inference from a well 
authenticated fact ; namely, that there are per- 
sons who do not perceive all colors. Colardeau 
was in this predicament. He sometimes em- 
ployed himself with painting, and one day made 
the ground of a picture scarlet, thinking to make 
it blackish ; when this was pointed out to him, 
he could not perceive any difference between 
these two colors. There exists at this day in 
England a distinguished man of science,* who 
perceived, on examining certain plants, that he 
had not the consciousness of every color ; and 
the annals of the Academie make mention of 
an entire family, who confounded green with 
red, so as not to be able to distinguish cherries 
from their leaves otherwise than by their form. 

* The experiment referred to by Arago, show- 
ing the duration of the impression on the retina, 
proves that the immediate cause of vision is not 
the presence of the visible object, but the spe- 
cific condition in which the retina is thrown by 
the light which proceeds from that object. If 
this condition exist when the object is not pre- 
sent, or be produced by any cause different 
from the object, vision will be equally produced, 
and the object will be seen where it is not 
present. The reality of this is fully proved by 
the rapid rotation of any visible object. The 
condition of the retina, whatever it be, which 
is produced by the presence of the visible ob- 
ject, continues for one-tenth of a second, sq that 
if such an object were suddenly concealed from 
the eye, it would continue to be seen for one- 
tenth of a second after such concealment. When 
the imagination is strongly excited, so as to pro- 
duce illusions in which unreal objects are per- 
ceived, it is probable that the membrane of the 
eye is excited as it would be if this fancied ob- 
ject were really present. If this be so, it would 
follow, that the brain and the membrane of the 
eye have what is called in physiology a recipro- 
cal sympathy. In all cases of ordinary vision, 
the membrane of the eye transmits the effect to 
the brain, but in the case just supposed, it is the 
brain which stimulates the optic nerve. 

On this principle is constructed the amusing toy 
called the Thaumatrope, contrived by Dr. Paris. 

It consists of a number of circular cards, hav- 
ing silk strings attached to their opposite edges, 
as represented in the following figures. By 

Fisr. 18. 




* I believe the person here alluded to is the late Dt, 
Dallon.— D. L. 



Arago and Lardner's Astronomy. 



13 



these strings, oue of the cards being twirled 
round with a certain velocity, both sides of it 
will be visible at the same time, and any objects 
traced on them, as a dog on one side and a mon- 
key on the other, may be perceived simulta- 
neously. Hence the parts of the picture being 



united, when it is whirled round, the monkey 
will be seen on the back of the dog. In this 
case the rovolving card becomes virtually trans- 
parent, so that the objects on opposite sides of it 
may be viewed together nearly as they would be, 
if painted on the two surfaces of a plate of glass 



LECTURE II. 

HISTORY AND DEFINITIONS. 



HISTORY OF ASTRONOMY. 

A dense cloud rests upon the cradle of all 
the sciences, but of none perhaps is the his- 
tory involved in so profound obscurity as that 
of astronomy. Coeval with the world, connected 
with the first wants of man, it must from the 
first have excited his curiosity and attracted his 
observation. But those first elements of the 
science, collected in various places, and at re- 
mote epochs, remained lost to the science, as 
tbey are for its history. 

We do not propose, therefore, to take astron- 
omy from its cradle, and follow its course down 
to our day, without ever losing sight of it for a 
moment amid the obscurity that rests upon its 
path ; but only to point to it at intervals on its 
way, as it gleams out from the darkness. 

The Chaldeans were probably the first who 
turned their attention to astronomy. This pas- 
toral people inhabited the delightful regions of 
Asia, the most beautiful portion of the globe. 
The habit of passing the night in the open air, 
the purity of the sky, the immensity of their 
horizon ; all these must early have solicited 
their attention to the movements of the heavenly 
bodies, and to the study of their imposing phe- 
nomena. 

Fx*om Chaldea it was not long before astrono- 
my spread into Egypt, that cradle of the arts and 
sciences : there it made great progress. The 
priests took it up, mingled it with religion, and 
employed it as an instrument of their sway over 
a credulous people, whom they labored to retain 
in ignorance and superstition. 

The Phoenicians were the first who applied 
astronomical observations to navigation. They 
had remarked that, amid the general move- 
ment of the sphere, one of the stars of the Lesser 
Bear appeared always to remain in the same po- 
sition. It was by this star they steered their 
course ; and such was their superiority, that in 
the time of Nechos, at a period when other peo- 
ple hardly dared to quit the coasts, they had set 
off from the Red Sea, circumnavigated Africa, 
and returned the third year to the mouth of the 
Nile. 

Nearly at the same epoch astronomy was in- 
troduced from Phoenicia into Greece by Thales. 
He taught the Greeks, who only knew how to 
observe the Great Bear, how much more sure a 
guide the polar star was to the mariner. He 
taught them the movements of the sun and moon, 
whence he derived the explanation of the length 



l of days, and the determination of the solar year. 
H^e was acquainted with the cause of eclipses, 
and even it appears with the means of predict- 
ing them ; for he acquired great celebrity by 
foretelling one that occurred on a day of battle 
between the Medes and the Lydians. 

Anaximander, one of his disciples, invented 
the terrestrial globe, had constructed at Sparta 
the gnomon that enabled him to observe the 
equinoxes and the solstices, and determined the 
obliquity of the ecliptic with tolerable precision. 
The Greeks were not slow in applying these 
novel ideas to the benefit of their navigation, but 
they were not grateful to the sage to whom they 
were indebted for them. They proscribed and 
would have put him to death, if Pericles had 
not succeeded in rescuing him from the super- 
stitious populace. His crime was his having 
taught that the universe is governed by immuta- 
ble laws. 

Pythagoras, who lived about five centuries 
before our era, greatly enlarged the science. He 
enriched it with almost all the grand views on 
which it reposes at the present day. It was he 
who first discovered the system of the universe 
to which Copernicus has bequeathed his name. 
It was he who first conceived the bold idea that 
the planets are inhabited globes, like that on 
which we move, and that the stars that people 
the immensity of space are so many suns des- 
tined to afford light and heat to the planetary 
systems gravitating toward them. He saw too 
in the comets, not fugitive meteors formed in 
the atmosphere, but permanent stars revolving 
round the sun, according to law3 peculiar to 
themselves. 

The first who taught the classification of cli- 
mates according to the days and nights was 
Pythias, who either originated or witnessed the 
origin among the Greeks of a decided taste for 
astronomy. No longer able to satisfy its cravings 
at Athens, they ascended to the sources of the 
science ; they went to study it in Egypt, aud 
Eudoxus brought back thence on his return new 
details, which he announced in several works. 
It was he who explained to the Greeks assem- 
bled at the Olympic games, and caused them to 
adopt, the famous cycle of nineteen years de- 
vised by Meton, to reconcile the motions of the 
sun and moon. The year of this cycle is still 
indicated in our calendars under the name of tho 
Golden Number. 

All the sciences are linked together, and mu- 
tually aid each other. Astronomy applied itself 



14 



Arago and Lardner's Astronomy. 



to the service of natural philosophy and geogra- 
phy, and lent them its light. Aristotle deter- 
mined the figure and size of the earth by astro- 
nomical observations. He derived proof of its 
sphericity from the appearance of the circular 
shadow it projects on the disk of the moon in 
eclipses, and from the unequal meridional ele- 
vation of the sun in different latitudes. 

Thus it was that the domain of astronomy be- 
came enlarged under the hands of these cele- 
brated philosophers. But among all the schools 
of antiquity in which this science was taught, 
that of Alexandria stood proudly and deservedly 
conspicuous. It collected skilfully a number of 
observations made with trigonometrical instru- 
ments, carefully described the constellations, 
determined with precision the positions of the 
stars and the courses of the planets, and began 
to account for the inequalities of the motions of 
the sun and moon. Hipparchus, of this school, 
determined the length of the tropical year with 
a precision not previously arrived at ; he came 
within four minutes and a half of the real time. 

Ptolemy, who is regarded as the first of astron- 
omers, lived in the second century after Christ. 
He has handed down to us, in his great Syntaxis, 
the principal observations and discoveries of the 
ancients. In this work he has given the theory, 
and tables of the motions of the sun, the moon, 
the planets, and the fixed stars. He had adopt- 
ed the theory which supposes the earth placed 
in the centre of the universe, which has received 
his name. The inaccuracies it involves did not 
hinder the great man's calculating the eclipses 
which should occur in the six ensuing centu- 
ries.- 

The Syntaxis was translated about the year 
326 by the Arabs, and called Almageste. Four 
centuries later the translation was rendered into 
Latin by order of Frederick the Second. Al- 
phonso of Castile then assembled the principal 
known philosophers, and caused them to draw 
up new tables, which were called Alphonsines. 

This patronage was not without its effect on 
the enlightened men of Europe. Astronomy 
led to favor and to fame; they cultivated it. 
Treatises were multiplied, and with them in- 
struments to facilitate observations. But the 
most memorable event of the period was the 
reproduction of the old system of the universe 
discovered by Pythagoras. It was Coper- 
nicus, born at Thorn in 1472, who revived it. 
He found that the system of Ptolemy, which 
supposed the world fixed, and the sun, the moon, 
and the planets, turning round this body in con- 
centric circles, was not in accordance with the 
phenomena. He observed that the difficulties 
with which it was embarrassed disappeared on 
admitting that the sun is a centre, round which 
the earth performs, like other planets, its annual 
revolution. This theory is based on arguments 
so incontestible that it is the only one at present 
taught in Europe. Unfortunately, Copernicus 
had not the satisfaction of witnessing the triumph 
of the doctrine he so ably defended. Persecuted 
by fanatics, a victim to the intrigues of the 
learned, it was not till long after he had com- 
pleted it that he published the book in which 
he had recorded the result of his observations. 
He saw the first copy of it, but in a few days 
afterwards he was no more. 



The only opposition of any moment offered to 
the system of Copernicus was made by Tycho 
Brahe, a celebrated Danish astronomer, who op- 
posed to it a theory of his own. His system 
differs little from that of Ptolemy ; it bears his 
name, however. He supposes that the earth is 
in the centre of the universe, and that the sun 
accomplishes its revolution around it in twenty- 
four hours. The planets do the same by him, 
but in periodical times ; Mercury first, as being 
at a lesser distance, then Venus, Mars, Jupiter, 
and Saturn, which move in the same manner. 
Some of his disciples, however, supposed that 
the earth was actuated by a diurnal motion round 
its own axis, that the sun and all the planets 
made their revolution round the earth in a year. 
We shall demonstrate the viciousuess of this 
system when we come to treat of that of Coper 
nicus. 

One of Tycho Brahe's disciples, Kelper, gave 
a great impulse to the science. Hipparchus, 
Ptolemy, and Copernicus himself, owed a great 
part of their information to the Egyptians, the 
Chaldseans, and the Indians ; they followed a 
beaten track ; but Kelper owed to his genius 
alone the discoveries that have rendered his 
name so celebrated: antiquity had not be- 
queathed to him any indications to du - ect him on 
his course. 

Galileo lived at the same period. While the 
one traced the orbits of the planets and discov- 
ered the laws of their movements, the other 
subjected to his researches the laws of motion 
in general, which had been neglected for two 
thousand years. It was by availing themselves 
of the labors of these two philosophers, that 
Newton and Huygens were enabled subsequent- 
ly to determine all the planetary motions. Gali- 
leo had proved beyond dispute that the earth 
possessed a diurnal and an annual motion ; but 
his doctrine was contrary to the received opin- 
ions of the day. The cardinals cited him to ap- 
pear, and, without regard to his age, his virtues, 
and his knowledge, they condemned him to per- 
petual imprisonment. 

Since the days of Newton, who brought it to 
its present advanced condition, astronomy has 
been continually cultivated by men who have 
become distinguished for their great acquire- 
ments and their admirable discoveries. 

* The epoch signalized by the labors of Co- 
pernicus, Galileo, and Kelper, was eminently 
favorable to the advancement of science. The 
darkness which enveloped the human mind for 
a long succession of ages had just been dispelled ; 
the revival of letters took place. The abuses 
which had been suffered to grow and spread in 
the church, led to that grand schism which ulti- 
mately resolved itself in the Reformation. The 
study of the sacred Scriptures, and the discus- 
sion of their historical records and doctrinal pre- 
cepts, became general ; and the emancipation of 
the mind soon spread from religion to science.. 
The same boldness which prompted Luther to 
question the dogmas of the church, stimulated! 
Galileo and Kelper to assail the dogmas of the- 
schools. The just method of regarding religious- 
questions derived from the spirit of the gospel,, 
was imitated in the chairs of the universities ; 
and the method of investigating the moral truths : 
promulgated by the voice of Revelation, was., 



Arago and Lardner's Astronomy. 



15 



happily applied to the discovery of the natural 
truths disclosed by the light of nature. 

* The hypothesis which placed the sun in the 
centre of the system,* had been at a remote pe- 

Fia 19. 




riod proposed by Pythagoras, but mankind was 
not yet sufficiently advanced for its reception. 
Even at the later date when Copernicus re- 
vived it, great were the obstacles to its fair con- 
sideration. The church, sensitively alive to the 
possibility of any discrepancy between the dis- 
coveries of science and what were supposed to 
be the intent and purport of the sacred Scrip- 
tures, was strongly opposed to it. Scarcely less 
intemperate was the opposition it received from 
the chairs of the professors. The earliest and 
by far the most illustrious of its supporters and 
defenders was Galileo. This philosopher, more 
distinguished by genius than discretion, iu advo- 
cating the new doctrines, came in conflict with 
the ecclesiastical authorities, and was summoned 
to Rome to justify himself before the pontiff and 
cardinals. Although in these proceedings there 
were circumstances which could not have occur- 
red in more enlightened times, yet, considering 
the spirit of the age and the little progress natu- 
ral science had made, Galileo was treated with 
erery regard for his position, and respect for his 
talents and acquirements. It is not true that he 
was sentenced to perpetual imprisonment ; nor 
is it probable that Arago could have made such 
a statement. The words of that astronomer in 
reference to this, must have been incorrectly 
reported. 

* Let us take a brief review of the memora- 
ble circumstances which attended discoveries, 
the results of which produced such an impor- 
tant influence on the progress of knowledge. 

* In the beginning of the seventeenth century, 

* The Copemican system places the sun in the centre, and 
all the planets with their moons revolving around him at 
different distances, and in different times as represented in 
the diagram. 



Galileo invented that species of telescope which 
is still distinguished by his name. The first dis- 
covery to which it led, was that the surface of 
the moon was not, as had been supposed, smooth 
and even, but on the contrary, rugged 
and mountainous. The discovery of the 
nebulas and stellar clusters, and the gene- 
ral character of the milky-way, followed. 
But these were lost in the more won- 
derful discovery of the fact, that the planet 
Jupiter was accompanied by four moons, 
which regularly revolved round him, as 
our moon revolves round the earth. So 
little prepared was the scientific world 
for this discovery, that it was with diffi- 
culty its reality could gain credence. A 
distinguished astronomer at Florence re- 
plied to its* announcement, that as there 
were only seven apertures in the head, 
— two eyes, two ears, two nostrils, and one 
mouth, — so there could be only seven- 
|p/ planets. He did not dispute the fact that 
/ the satellites were seen, but said that as 
they were invisible to the naked eye, 
they exercised no influence on the earth, 
and were therefore useless ; and being 
useless, could not exist ! 

* The image of the solar system pre- 
sented by the secondary system of Jupiter 
and his satellites, did not fail to impress the 
mind of Galileo more and more strongly 
with the validity of the Cope mi can 
doctrine. He accordingly now openly 
advocated that hypothesis", and urged irresistible 
arguments against the system of Ptolemy. The 
church took the alarm, and his presence at 
Rome was required before the Inquisition. 
That tribunal, in February, 1615, decreed that 
he should be ordered to renounce his obnoxious 
doctrines, and pledge himself not to teach, de- 
fend, or publish them for the future. Knowing 
that a prison would be the alternative, he yielded 
to the injunction, and was accordingly dismissed 
the court. 

* To keep the pledge thus extorted by the 
tribunal of the holy office was incompatible with 
the temperament of the man ; and accordingly 
he was no sooner i-eleased than he took an active 
and indiscreet part in opposing further proceed- 
ings of the same tribunal, which had for their 
object the proscription of Copernicus's wort, 
notwithstanding its dedication to the pontiff. 
Still the church was forbearing and tolerant to- 
ward Galileo. Every assurance which did not 
actually compromise its own consistency was 
given him. His friend and pupil, Castelli, was ap- 
pointed mathematician to the pope; and provided, 
he abstained from openly teaching or advocating 
in his published writings the offensive doctrines, 
according to his solemn pledge and promise, he 
was assured of safety and freedom from molesta- 
tion. 

* In noticing a name so illustrious, it is painfnl 
to be compelled to record conduct which, in a 
moral point of view, was not worthy of it. The 
truth of the Copernican system was fermenting 
in the active mind of the philosopher. .The si- 
lence imposed on him by his pledge was intole- 
rably irksome to him. He was impelled to the 
indulgence of the impulse of his mind by a bvs* 
tern of evasion. That which he dared not do 



16 



Arago and Lardner's Astronomy. 



openly, he attempted, by subterfuge and false- 
hood.' He composed a dialogue between three 
persons, in which they are made to discuss the 
pros and the cons of the two systems. The 
Copernican is nominally treated of as an inge- 
nius mathematical hypothesis, but in reality is 
established incontrovertibly as the system of 
nature, while the Ptolemaic system is assailed 
with all the weapons of reason, ridicule and wit. 
The license to print this book was obtained un- 
der false representations, and by trickery and 
deceit utterly unw.orthy of its illustrious author. 

* Galileo, as a matter of course, was again 
cited before the Inquisition. The charges against 
him on this occasion were not, as in the former 
case, unfounded. Independently of any ques- 
tion respecting the astronomical doctrines, he 
was now accused of breaking his solemn prom- 
ise, of deceiving and entrapping his own friends, 
and of procuring the license by indirect and un- 
justifiable expedients, and untrue representa- 
tions. These charges were, unfortunately, capa- 
ble of being proved ; and the philosopher was 
declared " to have brought upon himself strong 
suspicions of heresy, and to have incurred all 
the censures and penalties which are enjoined 
upon delinquents of this kind ; but from all 
these consequences he was to be held absloved, 
provided that, with a sincere heart, he would 
abjure and curse the heresies he cherished; and 
in order that his offence might not go altogeth- 
er unpunished, that he might be more cautious 
in future, and be a warning to others, it was 
decreed that his dialogues should be prohibited, 
and that he should be imprisoned during pleas- 
ure." 

* Galileo was accordingly obliged formally to 
renounce his errors, to deny the motion of the 
earth and the sun's stability, and to promise 
again never to teach or publish such doctrines ; 
after which he was consigned to the prison of 
the Inquisition. The popular anecdote of his 
stamping on the ground and exclaiming, in an 
under tone, e pur si muove, " it does move never- 
theless" has no authority to support it. 

* Galileo was not long subjected to the rigors 
of a prison. At the expiration of four days he 
was allowed to remove to the palace of the 
Florentine embassador, and soon afterwards re- 
moved to the Archi-episcopal palace at Sienna, 
from whence he returned to his own house at 
Arcetie, where he passed the remainder of his 
days. 

* Such are the principal circumstances of this 
memorable conflictbetween religion and science ; 
and when the spirit of the age is considered, and 
the impossibility of the ecclesiastical authori- 
ties recalling their first false step, without utter- 
ly abandoning their power and compromising 
their dignity, duly weighed, it will be admitted, 
that no greater real spirit of intolerance was 
manifested than is shown at the present day, by 
those who attack the researches in geology, and 
other parts of natural science. 

PRELIMINARY IDEAS DEFINITIONS. 

Astronomy treats of the motions, the distance, 
the size, the physical constitution, the eclipses, 
and all other phenomena of the heavenly bodies. 

Under the general name of stars are vulgarly 
comprehended all the bodies that fill the celes 



tial spaces ; but astronomy ranges them into 
several classes. 

In the language of astronomy, those are called 
fixed stars which in the revolution of the sphere 
seem always to occupy the same relative posi- 
tion, and to preserve the same distances the our 
from the other, For the greater facility in reco 
nizing and designating them, they are dividt 
into groups, called constellations. Each of thes«. 
has its proper name, derived from that of a mar 
or an animal, sometimes suggested by its form 
but almost always capriciously chosen. The 
utility of these names has continued them among 
us. To distinguish the several stars of a con- 
stellation from each other, they are classed ac- 
cording to their brilliancy or their apparent mag- 
nitude, and each class has a particular denomi- 
nation. Thus the most considerable is designated 
by A, and the others are marked according to 
the method of Jean Bayei, in the celestial maps 
published by him : this consists in designating 
each of them in the order of their magnitude by 
the letters of the Greek alphabet, beginning 
with a for the first, for the second, and so on. 
If the letters of the Greek alphabet are not suffi- 
cient, recourse is had to Roman letters, and even 
to the ordinal numbers, 1, 2, 3, &c. This no- 
menclature has been followed by all modern as- 
tronomers. 

Observations have shown that certain stars, 
besides the daily revolution which they have in 
common with the other heavenly bodies, have a 
motion peculiar to themselves, which alters their 
relative distances from the other bodies around 
them. These stars have received the name of 
planets, from a Greek word which signifies wan- 
dering. 

Herschel defines the planets, celestial bodies 
of considerable magnitude, and with slightly 
eccentric orbits, moving in planes that deviate 
but a few degrees from that of the earth, in a 
direct course, and in orbits very remote from 
each other, with vast atmospheres, w T hich yet 
bear scarcely any sensible proportion to their 
diameters. Some of these have satellites or 
rings. 

The planets are distinguished into primary and 
secondary. The primary planets are those which 
turn round the sun as a centre ; and the second- 
ary, more frequently called satellites or moons, 
are those that revolve round a primary planet as 
a centre, and are carried with it in its revolution 
round the sun. 

The primary planets again are divided into 
superior and inferior. The superior are those 
more remote from the sun than the earth, as 
Mars, Jupiter, Saturn, and Herschel ; the infe- 
rior are those that are nearer the sun than we, 
as Mercury and Venua. 

As for the planets recently discovered, Ceres, 
Juno, Pallas, Vesta, and those which may be dis- 
covered hereafter, Herschel has proposed to give 
them the name of Asteroides; under which 
name he includes those celestial bodies which 
move in orbits of any eccentricity around the 
sun, whatever angle their orbits make with the 
ecliptic, whether the motion of these bodies be 
direct or retrograde, whether they have or have 
not atmospheres. 

The following symbols are used to designate 
the planets in tables and on globes. Mercury § , 



Ar&go and Lardner's Astronomy. 



17 



5, the Earth @, M;irs J\ Vesta ft, Ju- 
no §, Ceres J, Pallas £, Jupiter %, Saturn T^, 
Hcrschel or Uranus M. 

1'ie ord$£ of a body is the course it describes 
roui.d that which serves it as a centre. The or- 
* : ts of the planets are ellipses of very slight 
fcetlricity ; those of the comets, on the con- 
fcry, are very eccentric : that is to say, they 
:eviate greatly from the circular form, and are 
bngthened considerably. 

■ An ellipse is a section of a right cone by a 
plane oblique to its base, but which does not 
tneet the base. To describe it, fix a circular 
thread by two points, and, keeping it at full 
stretch with the point of a pencil, carry the pencil 
all round: the two fixed points are the foci of the 
ellipse, and its eccentricity is its distance from 
the centre to the foci. 

The ecliptic is the orbit described apparently I 
by the sun round the earth, and in reality by the 
earth round the sun. 

The sensible horizon is a plane tangent to the j 
globe at a point where the observer is stationed. | 
It is the plane of the circle that bounds our views. | 
The rational horizon is a plane passing through 
the centre of the earth parallel to the sensible 
horizon. 

* The zenith is the point in the heavens imme- 
diately above the observer, to which a plumb line 
would be directed if continued upwards. 

* The nadir is the point immediately below 
the observer, and is diametrically opposite to 
the zenith. 

The colures are old terms designating two 
great circles of the sphere, which pass, the equi- 
noctial colure through the equinoctial points and 
the poles of the equator, the solstitial colure 
through the solstitial points and the poles of the 
ecliptic and of the equator. 

The meridian is a great circle of the sphere 
passing through the zenith and the poles. 

Azimuth is the arc of the horizon included be- 
tween the meridian and the vertical plane con- 
taining an object. 

Terrestrial longitude is the angle formed by 
two meridians measured by the arc of the equa- 
tor, or of its parallels intercepted between them. 
The longitude of a star is the arc of the ecliptic 
intercepted between the star and the first point 
of Aries. 

Terrestrial latitude is the distance of a place 
from the equator, reckoned on the meridian, and 
the latitude of a star is its distance from the 
ecliptic, measured on the great circle passing 
through the star and the pole of the ecliptic. 

Two planets are in conjunction when they 
have the same longitude ; they are in opposition 
when their longitudes differ by 180°. 

Declination is the distance from the equator 
of the parallel described by a star ; it is south- 
ern or northern, according as the star is on one 
or the other side of the equator. 

The poles are the extremities of the axis of a 
circle. 

The nodes are the points where the orbit of a 
planet cuts the ecliptic. The node whence the 
planet rises toward the north above the plane of 
the ecliptic, is the ascending node; that whence 
it descends toward the south is the descending 
node. The line joining the two is called the line 
of the nodes. 

2 



The solstices are the two extreme points of 
the sun's apparent course north and south of the 
equator. 

The tropics are parallels to the equator cor- 
responding to the sun's position at the solstices ; 
they are the limits of the torrid zone. 

The sphere is the great concavity apparently 
formed by the space surrounding our globe, in 
which we see the celestial bodies. It appears 
to revolve upon the line joining the two poles. 
Apogee is that point in the moon's orbit in 
which it is farthest from the earth, and its peri- 
gee is that in which it is nearest to it. 

A planet's apsides are those points in its orbit 
in which it is at its greatest or least distance 
from the sun. The first of these points, that is, 
the point of greatest distance, is called aphelion, 
the other perihelion. The line joining them, 
and. passing through the sun's centre, is called 
the line of the apsides. 

Syzygy is the name given in common to the 
moon's opposition to, and her conjunction with 
the sun. 

The equator is a great circle, every point in 
which is equally distant from the poles. 

Those places with respect to which the poles 
are situated in the horizon, are said to have a 
right position of the sphere. Those whose hori- 
zon coincides with the equator, have a parallel 
position of the sphere. For all intermediate 
places, the position is oblique. 

A parabola is a section of a cone by a plane 
parallel to the side of the cone: it is therefore 
an open curve. 

Parallax is the angle formed by the two lines, 
in the direction of which a star would be seen 
at the same instant from the centre of the earth, 
and from a point on its surface. 

The zodiac is a zone extending about nine 
degrees on each side of the ecliptic. It is di- 
vided into twelve parts called signs, and each 
sign into thirty degrees. The^signs of the zodiac 
have each a special name and symbol. 

* °f Aries (the ram) extends on the ecliptic 

from 0° to 30° 

^ Taurus (the bull) extends 30° " 60« 



U Gemini (the twins) 


60° 


" 90° 


53? Cancer (the crab) 


90? 


" 120° 


SV Leo (the lion) 


120° 


" 150° 


n# Virgo (the virgin) 


150° 


" 180° 


=2: Libra (the balance) 


180° 


' 210° 


1t\ Scorpio (the scorpion) 


210° 


'240° 


% Sagittarius (the archer) 


240° 


'270° 


VJ Capricornus (the goat) 


270° 


1 300° 


%Z Aquarius (the waterman^ 


>300° 


'330° 


^£ Pisces (the fishes) 


330° 


'360°or0 



They are situated in the foregoing order, 
reckoning from west to east, and this is called 
the order of the signs. As an assistance to the 
memory, the following Latin hexameters have 
been constructed: 

Sunt Aries, Taurus, Gemini, Cancer, Leo, Virgo, 
Libraque, Scorpius, Arcitenens, Caper, Amphora, Pisces: 

The etymological explanation of these names 
has given rise to numerous discussions, which 
the Egyptian Institute has lately brought to a 
close, by showing that the names, now univer- 
sally adopted wherever astronomy is cultivated, 
are derived from comparisons made by the 
Egyptians betwen celestial phenomena and ter- 



IS 



Arago and Lc 



r&ner 



istronomy. 



restrial ones, for the most part purely of a local 
nature, and belonging exclusively to a part of 
their country. The following brief abstract of 
this curious investigation cannot fail to prove 
interesting to the reader. 

I. Capricornus (Caper) VJ. 

The first month of summer: it extends from 
the 20th of June to about the 20th of July. 

In Greek, Er^i, eizrfi (Alberti, Fabricii Me- 
nologium.) 

Coptic, Epep (Lacroze, Lexicon Egyptiano- 
Latiaum.) 

Arabic, HebbCbi, hebbCb. 

Latin. These different names may be thus 
interpreted: Caper, dux gregis, qui ccepit, spe- 
cies apparcns aqua, cvigilatio, motio hue et illuc, 
aurora. 

The Arabic verb hebbeb or kabdb signifies 
capit, evigilavit, experrectus fuit e somno , flavit 
venlus, vacillavit, hue et illuc motus fuit, insiliit 
in f avi I la m. 

The following is the explanation of the Latin 
phrases equivalent to the Arabic and Coptic 
words. 

Caper gives name to Capricorn, one of the 
twelve signs of the zodiac. 

Dux gregis, qui ccepit. Capricorn opens and 
begins the year: he is the leader of the celes- 
tial animals, as on earth he is the leader of the 
flock. 

Species apparens aqua: commencement of 
the rising of the Nile, which usually does not 
make its appearance till ten days after the sol- 
stice. 

Qui evigilavit, experrectus fuit e somno, points 
to the longest day : the sun, or the animal that 
represents it, is awake, and rouses the world at 
ihe hour in other seasons appropriated to sleep. 
Qui vacillavit, qui hue et illuc motus fuit: the 
hesitating motion of the sun when arrived at the 
solstice. 

Qui flavit ventus: the northern winds blow 
for fifteen days at the period. The almanac of 
the Egyptians announces their arrival. 

Aurora: this proves that the Egyptian year 
commenced at the aurora of the goat, at the 
dawn of the first day of summer. Finally, Epi- 
phi or Epephi, according to Herodotus, was 
probably one of the twelve astronomical gods of 
the Egyptians, for he says, book ii. chap. 38, that 
oxen were sacred to this god. 

II. Aquarius 2£. 

Aquarius was the second month of summer, 
and lasted from the 20th of July to the 20th of 
August. 

Greek, Meo-opt, Meo-o-opi, Mfo-wis^, TS/Leawpij, Me- 
nologium. 

Coptic, Mesore. 

Arabic, Mesour, misr, vas aqua paulatim lac 
suum reddens. 

The Arabic verb meser is translated prabuit 
paulatim, emulsit quicquid esset in ubere. The 
addition of a final y makes the impersonate 
word mesour?., signifying aquarius. 

Paulatim lac suum reddens, etc., agrees per- 
fectly with the figure of aquarius in the zodiacs 
of Essori and Denderah, in which the vessel 
very slightly stooped lets the water it contains 
slowly escape. 



Emulsit quicquid esset in ubere. It is during 
this month or thereabouts, that the sources of 
the Nile give out their full complement of water. 
The Egyptians regarded this fluid as equally 
mild and nutritive as milk. The inundation 
augments during this month. 

III. Pisces X- 

The third month, from the 29th of August to 
the 20th of September. 

Greek, Tw0, Ouvd, Qwdi, <pdu 

Coptic, Thoout. 

Arabic, Thohoul. Ambulatio piscis, incessus, 
reciprocatus ultro retroque in se rediens. 

The Arabic verb tona signifies peragravii r'e~ 
gionem, opplevit pute.um. From hout, a fish, 
comes the verb hat. circumnatavit. 

Ambulatio, &c. exhibits the fishes moving 
backward and forward in the waters that cover 
the laud. 

Opplevit puteum, marks the inundation, cov- 
ering all the low places, for it is spread over the 
[whole of Egypt: the festival of Isis was fixed 
in this month, because it was also the season of 
the festival of the Nile, celebrated by opening 
the dikes. For this reason the month was 
sometimes called fotouh, aperlura per term, 
superficiem fluentis aqua opening of the dikes. 

A passage in Sanchoniatbo, preserved by 
Philo, says that messori gave birth to ihoth; and 
in reality, we see it is messori, or the rise of the 
Nile, that produces touhout, the expanse of 
water over the face of Egypt, in which the fish 
move about. 

IV. Aries °f. 

The first month of autumn, beginning the 20th 
of September, ending the 20th of October. 

Greek. *$}au>pi, raocbi. mu. 

Coptic, Paopi. 

Arabic, Fofo, foafi, hadus, velo.r, vox qua 
greges increpantur. 



The Arabic verb signifies 



mcrepuit gregem 



dicens fafa. 

The Hebrew verb fafa signifies obtene- 
brescere. 

Vox qua greges increpantur: as the waters 
retire, the ram again returns to the pasture, 
leading the flocks that have been held captive 
during the inundation. 

Obtenebrescere : the day diminishes more and 
more, as is the case in the month beginning at 
the autumnal equinox. 

V. Taurus #. 

The second month of autumn, from the 20th 
of October to the 20th of November. 

Greek, AOwp, aQopi (6cj«/), Eusebius.) 

Coptic, Athor. 

Arabic, Thaur, athour, taurus, tauri. 

The verb athor, aravii, submovit terrain. 

Tillage is not performed in Egypt till other 
countries have done sowing, in the month of 
November. 

VI. Gemini FL 

The third month of autumn, from the 20th of 
November to the 20th of December. 
Greek, Xouk, x oiaK i KCn > : > Knxos. 
Coptic, Chorak. 
Arabic, Chori?:, amore flagrante^, a?nalore$ 



Arago and Lardner's Astronomy. 



19 



In the Egyptian zodiacs, this sign is repre- 
sented by a young man and a young girl: in this 
month seeds heat and germinate; the Greek ap- 
pellation for this sign is but a vague one, Si6vjxoi. 

VII. Cancer 5ZE« 

The first month of winter, ftom the 20th of 
December to the 20th of January. 

Greek, Tv f3c 

Coptic, l 1 obi. 

The verb teby, amovit, avertit: the verb teb, 
reversus, conversus, fuit, respv.it. The roots 
accord very well with the retrograde motion of 
the suu at the winter solstice. 

VIII. Leo ft. 

The second month of winter, from the 20th of 
January to the 20th of February. 

Greek, Msy/p, Me^ei^, Mc^o?. 

('optic, Cher?/ or Mechery. 

The verb cker, acquisivit, collegit; meeker, 
pars se^cfis, or meeker, protulit frondes, ramos; 
amcker, plantas suas extulit terra, inflatus tur- 
kidus fuit. 

In Eerypt the earth assumes its most beautiful 
aspect in the month of February; a part of the 
Harvest is already begun: the king of animals 
was chosen to typify the strength and the mag- 
nificence of nature at this period. 

IX. Virgo Ti£. 

The third month of winter, from the 20th of 
February to the 20th of March. 

Greek, 3>a//£u&>0. 

Coptic, Pkamenoth. 

Arabic, Famenotk. Mnlier fescunda et pulchra, 
qu/c vcnd.it spicam, frumcuium, et quod portatur 
inter duos digitos. 

This word is compounded of famij, one who 
sells ears of corn, and seeds of all kinds, the ear 
or stalk of which can be earned between two 
lingers, and enoth, a beautiful fruitful woman. 
In the Egyptian zodiacs Famenotk, or the fruit- 
ful woman, holds an ear of corn in her hand: 
what led the Greeks into the error of calling 
this sign iraptpevos, is that the Egyptian word sig- 
nifies " endowed with beauty," but it also in- 
volves the idea of fruitfulness. 



X. Libra =2:. 

The first month of spring, from the 20th of 
March to the 20th of April. 

Greek, QapnovOe. 

Coptic and Arabic, Faramour, mensura, regula 
eonfecta temporis. 

This month answers to the vernal equinox 
and the equality of the days and nights. 

XL Scorpio r\. 

The second month of spring, from the 20th of 
April to the 20th of May. 

Greek, Ha%&>K. 

Coptic, Packons. 

Arabic, Backony, prostravit humi venerium,, 
aculeus scorpionis. This word is compounded 
of bach, prostravit, kumi stravit, which in all the 
Oriental languages signifies putruit, Icesit, pravus 
\fuit, or putrido, -malum,, morbus, and homily, 
veneuum, aculeus scorpionis terror. It is charac 
teisistic of the second month from the vernal 
equinox, the heat of which stimulates venomous 
reptiles, and excites disease and pestilence 
The root hama also signifies ferbuit dies, the 
days become burning. 

XII. Sagittarius J . 

The third month of spring, from the 20th of 
May to the 20th of June. 

Greek, Tlavvt, traoyvt. 

Coptic, Paons. 

Arabic, Fayne or fenni, extremitas sceculi tern. 
pons, kor(£, Faijnan, fenan, nomen equi, onager 
varii cursus. 

The root farm signifies propellit, impulil; 
faijni signifies propulsaior, ivipuisator. 

Extremitas : last month of the Egyptian year 

Nomen equi: onager: name of a quadruped. 
Propulsator indicates its action. In the Egyp- 
tian zodiac the animal is figured -with the body 
of a quadruped and with a double head ; one of 
a lion, the other of an armed man about to dis- 
charge an arrow : it seems to drive forward the 
animals that precede it and to check those that 
follow; everything indicates that it will soon 
reach the goal toward which it is tending, and 
that its course is on the point of terminating. 



LECTURE III. 

ASPECT OF THE HEAVENS, 



ASPECT OF THE HEAVENS APPARENT MOTIONS OF 

THE HEAVENLY BODIES. 

When we cast our eyes on the heavens, we 
behold a vast hemisphere expanding over our 
heads, whose centre we seem to occupy, and 
which appears to join the horizon at its base. 
By day this immense vault is lighted by a bril- 
liant disk, which, issuing from the regions of the 
east, traverses it majestically, descends, and dis- 
appears again in the west. The feeble light it 
leaves behind is soon extinguished, and then 
appear from all sides in the immensity of space 



! a multitude of brilliant points, of various dimen- 
j sions, whose numbers augment as the darkness 
increases. The motions of these bodies add still 
more to the beauty of the spectacle. While 
some of them, moving in the same direction as 
the sun, proceed like him toward the west, 
and there sink beneath the horizon; others again 
make their appearance in the oa».t, a.i.u- .'ho 
vault of the heavens, and disappear in their Turn 
in the quarter where the sun passed from oar 
view. All do not, however, thus aink below 
the horizon; some there are that for us never 
reach this circle, and whose course may be ob- 



20 



Arago and Lardner's Astronomy. 



served all the night through; one of them even 
appears constantly immovable. Again, while 
some describe a vast arc in the heavens., others 
traverse a small arc above the horizon, and some 
even do but rise and disappear. Such are the 
phenomena of the rising and the setting of the 
stars. It is this general movement which the 
starry sphere accomplishes in a day and a night, 
that has received the name of the diurnal mo- 
tion of the sphere. 

In this revolution of the sphere, the stars, as 
they undergo the motion we have just described, 
appear at the first view to retain the same re- 
lative distances. But more accurate observa- 
tions soon show us, that, whereas the greater 
number of the heavenly bodies do indeed al- 
ways preserve their relative positions, some of 
them possess a peculiar motion of their own, 
which carries them successively from one con- 
stellation to another. This is called the proper 
motion of the planets. 

The sun, like the planets, has a motion of its 
own, for we see it rise and set successively in 
different points of the horizon. At the end of 
June it rises near north, remains a long while 
above the horizon, and approaches nearer the 
zenith; whereas, at the end of December, it 
rises nearer the south, keeps at a distance from 
the zenith, and describes but a small circle 
above the horizon. To this proper motion of 
the sun we owe the variety of the seasons and 
the inequality of the days. 

The moon's motion, and the aspect she pre- 
sents at different periods of her course, are still 
more remarkable. First, she begins to show 
herself on the western side of the heavens at lit- 
tle distance from the sun, under the form of a 
crescent, which enlarges as the moon's distance 
from the sun increases, until at last it rises in the 
east the moment the sun sets in the west; her 
face is then exactly circular. She now bends 
gradually more toward the east, rises further and 
further so every night, till at last she is as near 
the sun in the east as she had been in the west. 
She then shows herself in the morning a little 
before him, as in the first part of her course she 
had appeared a little after him. These different 
phases are run through in the space of a month; 
after which they are again repeated in the same 
order. 

Sometimes, finally, we observe in the heavens 
luminous bodies quite different from those of 
which we have yet spoken, and which, from 
the various changes they undergo, have always 
been objects of popular wonder and curiosity. 
At first very small, and of little brilliancy, they 
soon acquire considerable dimensions, and ex- 
hibit a luminous train of very variable extent 
and splendor: these are comets. Possessed of 
motions of their own, whose direction is capable 
of change, the nearer they approach the sun, the 
more do their tails become developed in extent 
and brilliancy: at last, their lustre and their 
magnitude diminish with more or less rapidity, 
and they disappear wholly from our eyes. 

On contemplating this revolution of the sphere, 
two questions present themselves to our minds. 
Does each star always employ the same time to 
complete its revolution? and is its motion uni- 
form, that is to say, does it describe equal spaces 
in equal times? 



To solve the first of these questions, no more ! 
jj is necessary than to direct toward any one star 
ij a telescope immovably fixed in a suitable po- 
ll sition. On counting the time elapsing till the 
same star reappears in the field of the telescope, 
we soon find that the duration of the revolution 
is absolutely the same, whenever it takes place, 
and whatever be the star. The space of time 
elapsing between two consecutive returns of a 
star to the same meridian constitutes a sidereal 
day. 

The second question may be answered by 
means of an apparatus called a parallactic in- 
strument. It consists of a graduated circle im- 
movably attached to an axis passing through its 
centre, and perpendicular to its plane ; this axis 
is also the diameter of a movable circle, which 
is, therefore, constantly perpendicular to the 
first: this second circle, which is furnished with 
a telescope capable of assuming any inclination 
to the central axis, as it turns upon this axis, 
gives motion to a needle, that marks off on the 
first circle the horizontal axis traversed by the 
second. If the telescope be now directed to- 
ward a star constantly visible, it will be neces- 
sary, if we would not lose sight of it in the cir- 
cle it describes, to put the axis of the instrument 
in the same direction as that of the heavens, and 
give the movable plane a motion corresponding 
to that executed by the star: then, if we note 
very exactly the intervals of time that elapse 
while the movable plane traverses equal arcs oiV 
the fixed plane, we shall find that these inter- 
vals are all equal. To estimate, therefore, how 
much a star has changed place, it is indifferent 
whether we take for our measure the arc it has 
traversed, or the time it has spent in travelling 
it, when we have once established a known re- 
lation between these two data. Thus the sphere 
completing its revolution in twenty-four hours, 
and all the diurnal circles being divided into 
three hundred and sixty degrees, the stars de- 
scribe arcs of fifteen degrees hourly. We must 
remark, however, that these circles not being 
equal, their divisions do not coincide, and that 
in order to compare the results, we must deter- 
mine their relative value. 

It is a very common error to suppose that the \ 
stars are visible by day from the bottom of a 
well. Thej can only be seen by day with the 
help of telescopes, or by mounting in a balloon, 
or from the summits of lofty mountains. The 
reason why they are invisible to the naked eye 
is, that the sun's rays, reflected by the atmo- 
sphere, form a luminous curtain which prevents 
our seeing them, their light being incomparably 
too weak. In point of fact, it is enough that a 
light be sixty times weaker than another, to 
make it imperceptible to our eyes in presence 
of that other. This fact may be illustrated by a 
very simple experiment: place between two 
lighted candles an object that will thus project 
two shadows; then remove one of the candles 
to such a distance, that the light it casts on the 
body be but a sixtieth of what it was before, a 
thing which may be easily effected, since we 
know that the intensity of light varies inversely 
as the square of the distance. The shadow pro- 
jected by the light made thus remote will no 
longer be visible: if motion, however, takes 
place, it will become perceptibie. This is the 



Arago and Lardner's Astronomy. 



21 



principal reason why stars are visible by day- 
light through optical instruments ; for, since these 
instruments magnify, they prodigiously enlarge 
the distances traversed, and proportionally ac- 
celerate the motion. 

Besides the peculiar motions which enable us 
at first to distinguish the planets and comets 
from the fixed stars, another difference soon ar- 
rests our attention, namely, the scintillation or 
twinkling exclusively observable in the fixed 
stars: this is a change in the intensity in their 
light accompanied by a change of color. To 
understand this phenomenon, we must have re- 
course to a remarkable discovery recently made 
in the properties of light. If we cailse two rays 
of light having a common origin to meet in one 
point, they will not always combine to produce 
a gi-eater volume of light; on the contrary, it 
may happen, if we make them traverse different 
distances, or pass through media of different 
densities, that under the proposed conditions, 
these two rays, instead of mutually aiding, will 
mutually destroy each other, so that, however 
paradoxical it may seem, we shall have pro- 
duced darkness by adding light to light. This 
is the phenomenon of luminous interference. By 
it we explain the twinkling of the fixed stars. 
The different portions of the atmosphere contin- 
ually varyiug in density, realize the conditions of 
the phenomenon of interference, and thus inter- 
cept some of the rays composing the white light 
of the stars, leaving only the other rays to reach 
our eyes, and present them with a feeble and 
differently colored image. 

The reason why the planets do not twinkle 
is, that they are of a certain magnitude. 

The aspect of the heavens varies with the po- 
sition of the observer. Let us suppose him sta- 
tioned at one of the poles of the earth — the north 
pole, for instance. In this situation his zenith 
will be the northern celestial pole, and his ra- 
tional horizon will coincide with the equator. 
All the stars whose declination is northern, that 
is to say, all those included between the equator 
and the north pole, will appear to move in cir- 
cles parallel to the horizon. Those whose place 
is in the equator, will sweep the horizon, and 
all those whose declination is southern will re- 
main constantly invisible. The parallelism of 
all these motions to the horizon has obtained for 
this position, as we have already said, the name 
of parallel position of the sphere. 

Now let us suppose the observer transported 
to the equator ; his rational horizon will pass 
through the poles, and in this position he will 
perceive the stars during the whole time they 
employ in traversing half their diurnal circles, 
and the planes of all these circles will be per- 
pendicular to the horizon. This is the right po- 
sition of the sphere. 

If the observer then move toward one of the 
poles — the northern, for example — this pole will 
appear gradually to rise above the horizon, and 
the south pole to sink below it in the same pro- 
portion. Suppose the observer removed, for in- 
stance, 30 degrees from the equator toward the 
north pole, his zenith will be F, the great circle 
HOR will be his horizon, the plane of the equa- 
tor EOZ will be 30 degrees removed from the 
zenith F, and consequently 60 degrees distant 
from the horizon. The pole P will be elevated 




30 degrees, measured by the angle HCP, and the 
pole P' will be depressed by the same quantity 
below this plane. It follows from this construc- 
tion that the distance from the zenith to the 
equator, or the latitude of the place, is always 
equal to the elevation of the pole above the 
horizon. In this situation the circles described 
by the stars are inclined to the horizon, whence 
this position of the sphere derives its name of 
oblique. 

In following the stars of the sphere in their 
course, we have seen them all rise successively 
above the horizon, and then sink below it. At 
what point is it that the star will cease to rise? 
How is this to be determined? 

There are several methods of arriving at the 
solution of this question: the following, founded 
upon corresponding heights of the sun, is per- 
haps the simplest. 

Upon a surface exactly horizontal (of which 
we can assure ourselves by means of a spirit 
level) we place a vertical style, from the foot of 
which as a centre we describe several circles on 
the horizontal surface. On each of these we 
mark the points corresponding to the extremities 
of the shadows projected by the sun at different 
heights before and after noon; we then divide 
the arc comprised between the two points which 
the shadow has marked on each circle, and thus 
we obtain a line, which, passing through the 
foot of the style, determines the plane in which 
the sun is found, when he has reached the high- 
est point in his course. This instrument is called 
the gnomon, and the plane which it serves to de- 
termine, the meridian, and which passes through 
the zenith of the place, and through the poles. 

Another method, also very simple, is that of 
the measure of time : but it requires the aid of a 
transit instrument, or meridian telescope, which 
we are the more induced to describe, as it is of 
frequent use among astronomers. 

This instrument consists, like the usual astro- 
nomical refracting telescopes, of a cylindrical 
tube furnished with an object-glass and eye- 
glass. In the focus of its object-glass is placed 
a diaphragm pierced in the middle, and intend- 
ed to prevent the passage of all the rays except 
those near the axis, so as to render the image 
more distinct. In the same situation are Jixed. 
on a movable metallic .plate, extremely hue 



22 



Arago and Lardner's Astronomy. 



wires, dividing the field of view into four equal 
parts. Iu the micrometer, these wires are usu- 
ally of the number of five vertical and parallel, 
and one horizontal. This instrument, fixed with 
the utmost possible stability on upright supports, 
is so constructed as to be only capable of mov- 
ing in one vertical plane. 

To determine the meridian, the instrument is 
placed in a vertical plane, the telescope is di- 
rected upon a star constantly visible, the in- 
stants of its greatest and least heights are noted, 
and the time elapsed between the tw r o transits 
of the star is counted with a very exact chrono- 
meter. Almost always, if we have chosen a 
vertical plane at hazard, we find a great differ- 
ence between the two portions into which its 
course is thus divided, the one being greater 
than a semi-revolution, that is to say, than twelve 
hours sidereal time ; the other less. It will be 
sufficient to kuow this difference, to enable us 
by repeated essays gradually to adjust the in- 
strument to the plane which shall accurately di- 
vide, into two equal portions, the diurnal circle 
of the star. 

There are also several methods for expressing 
the position of the stars. Two of these are par 
ticularly in use. 

The first consists in measuring the angles 
formed by the vertical plane passing through 
each star with a meridian, to which we refer 
the distances of these stars. 

We begin by fixing the height of the star ob- 
served, on the vertical plane in which it is situ- 
ated, by means of the mural quadrant. This is 
a sector furnished with a movable telescope, in 
•whose focus there is a micrometer consisting 
only of two movable wires, the one vertical, the 
other horizontal: the radius of the quadrant 
must be placed exactly vertically in the plane 
of the meridian, and must be set at on the 
scale at the curved edge of the p!ate on which 
the radius moves. The vertical thread serves 
to direct the optic axis into the plane of the ra- 
dius, an indispensable precaution, in order that 
the arcs measured by the limb may be equal to 
those described by the optic axis. At the mo- 
ment when the star enters the field of the tele- 
scope, it is made to pass by means of a suitable 
mechanism along the horizontal wire, and when 
its centre touches the vertical wire, it is exactly 
in the plane of the meridian. We then read off 
upon the limb the arc subtended by the angle 
formed by the vertical radius and the visible 
ray: this angle is the zenith distance, the com- 
plement of the meridian altitude. 

The next thing to be known is the angle 
formed between the vertical of the observed 
star and the meridian; this angle is called trie 
star's azimuth, and is either east or west. It 
may be found by accurately noting the time of 
its passage across the meridian, and the time of 
its being in the vertical where it is observed: 
the interval between these two times enables us 
to calculate the angle. This method, which is 
extremely simple, is pretty frequently employed. 

The zenith distance and the azimuth of a star, 
elements necessary for ascertaining its position, 
may also be obtained by means of an instrument 
called an altitude and azimuth circle, consisting 
of two graduated circles: one of which, horizon- 
tal, represents the horizon: the other, furnished 



with a telescope having a micrometer, is per- 
pendicular to the former, and moves freely upon 
a vertical axis. At the moment we wish to ob- 
serve the star, we bring the centre of the cross 
wires to bear on it, having first carefully ad- 
justed the last-named circle in the vertical plane 
of the star. This circle then indicates the alti- 
tude of the star above the horizon, and its zenith 
distance which is the complement of that quan- 
tity, while the horizontal or azimuthal circle 
marks the azimuth at the moment of the ob- 
servation. 

Zenith distances and azimuths form, as we 
see, a system of angles, by means of which it is 
easy to fix the position of the stars with extreme 
j precision. But this method is subject to one in- 
convenience which has led to its almost entire 
abandonment: this is, that the zenith and the 
azimutns varying as often as the observer chan- 
ges his horizon and his meridian, there is thus 
J no fixed point to which every observation may 
I be referred, and there is no common point of 
I comparison between the several positions. For 
! this reason, the following method, called that of 
■ right ascensio?is and declinations, is generally 
preferred. 

In this method, it is enough to know the her 
ary circle of the star, and its place in this circle. 

The place of the star in the horary circle is 
determined by means of the instrument we have 
already described for measuring meridian alti 
j tudes. With this instrument we ascertain the 
distance of the star from the pole, and from this 
the complement thereof, its distance from the 
equator, which we term its declination; on this 
account, horary circles are sometimes called 
circles of inclination. 

Declination is counted from up to 90 de- 
j grees, and is either (north or south) in reference 
to the equator. 

As for the position of the horary plane, it is 
determined by the angle it makes with a given 
horary plane. If the angle formed by the meet- 
ing of these planes be measured by an arc of the 
equator, this arc is what is called the right as- 
cension of the stai\ It is determined by observ- 
ing the time that elapses between the passage 
of the star across the meridian, and that of the 
horary plane selected to reckon from. Astrono- 
mers designate with the sign °| c , the point from 
which they begin to count right ascension ; this 
is the point where the sun cuts the equator, 
when he reascends from the southern tropic to- 
ward the northern. 

Right ascension then is the angle wdiich the 
horary plane of a star forms with the meridian, 
at the moment when the point assumed in Aries 
°I°, that point in which the sun appears to us in 
spring, is situated in the plane of the meridian. 
Right ascension is always counted from west to 
east, and from up to 360 degrees, or an entire 
circumference. This system of lines for deter- 
mining the position of stars presents, it is ob- 
vious, many analogies with the preceding one; 
but it differs essentially from it in this respect, 
that the position of the stars being indicated 
with relation to circles of the sphere invariably 
fixed, since they are in fact the celestial equator 
and a fixed meridian, observers, wherever situ- 
ated on the earth's surface, may all refer their 
observations to it, and compare together the re- 



Arago and Lardner's Astronomy. 



23 



suits they have obtained. Declination and right 
ascension being known, every relation of place 
and distance in the celestial sphere may be dis- 
covered. 

The foregoing remaks will enable us to under- 
stand the method of obtaining a catalogue of 
stars by means of a transit or any other suitable 
instrument. We determine the moment when 
any known star whatever passes the meridian; 
we note exactly the hour, minute, aud secoud of 
the passage, reckoning from on the astronomi- 
cal clock" We do the same by all the other 
stars, as they arrive at the plane of the meridian. 
Thus we become acquainted with the differences 
of their right ascensions: we learn also the alti- 
tude of each of them. Having obtained, these 
data, we can easily lay down their relative po- 
sitions to each other, and we shall thus possess 
a celestial map. on which will *be traced the 
various groups of stars forming the constellations. 
The first celestial maps were of great antiquity. 
Hipparchus was die first who constructed them, 
and as the relative distances of the stars have 



undergone no sensible change since the earliest 
observations, they may always be employed in 
studying the heavens. 

The same point which serves to count right 
ascension from, is also the starting-point of si 
j dereal time; that is, we count Oh 0' 0'' sidereal 
time, at the moment of its meridian transit. 

It will now be readily conceived that nothing 
can be more easy than to ascertain the hour of 
the day in sidereal time, the elevation of the 
pole at the place occupied by the observer be- 
ing previously known. It will be enough to 
observe the zenith distance of a known star, and 
to calculate rs horary angle, counted, for in 
stance, from the superior meridian, in the direc- 
tion of the diurnal movement from to 360 de- 
grees, adding this angle to the right ascension c f 
the star, and rejecting entire circumferences, if 
there be any. The remainder converted into 
time will express the distance of the meridian 
from the point of the heavens assumed as the 
starting-point, that is to say, the hour in sidereal 
time. — \_Biot. Astr. Phys. 



LECTURE IV. 

THE FIXED STARS. 



Under this denomination, are comprised all 
those bodies of the sphere which appear al- 
ways to retain their relative positions: which 
appear, we say, because modern observations, 
particularly those of Herschel, have proved 
the occurrence of changes in their mutual posi- 
tions, whence we must conclude that the fixed 
stars are also subjected to motions, very slow 
indeed, and scarcely perceptible. Their num- 
ber at the first view appears immense, because 
they are scattered and confused, and cannot all 
be included together in the field of vision. We 
may easily satisfy ourselves that the number of 
those that can be seen with the naked eye is 
very limited, and amounts to scarcely more than 
a few thousands. All we need do is to take a 
portion of the heavens and count those it con- 
tains: we shall hardly be able to see more than 
500 at a time, but with the help of telescopes 
their number increases beyond expression. 

Their distribution in the heavens in groups or 
masses has suggested the idea of arranging them 
into constellations. These, as we have already 
seen, are systems of stars distinguished from 
each other by letters and figures. Hipparchus 
has bequeathed us a general table of the constel- 
lations reckoned in his time: they are forty-eight 
in number, twelve in the zodiac, twenty-one 
north, and fifteen south of it. At the present 
day, their number is considerably augmented. 
At the end of the volume will be found a table 
of the constellations, with the number of stars 
included in each. 

Kepler threw out a very ingenious suggestion 
respecting the dimensions and the distances 
of the fixed stars. He remarked that there are 
on the surface of a sphere only thirteen points 
equally remote from each other and from the 



centre, and supposing the nearest fixed stars 
to be as distant from each other as they are from 
the sun, he comes to this conclusion, that there 
are rigorously but thirteen stars of the first 
magnitude. At twice the distance from the sun 
there may be four times as many/ and so on. 
This method of calculation agrees pretty nearly 
with the number of the stars of the first, second, 
and third magnitudes. 

In clear weather, when the stars are very dis- 
tinct, we see in several parts of the celestial 
sphere whitish spots shedding a faint light. On 
examining them with an instrument of high 
magnifying power, we discover in them a mul- 
titude of little stars set very close together; 
it is the light they give that occasions the ob- 
served spots. The milky-way, that broad zone 
spanning the vault of the heavens, is itself but 
an assemblage of similar nebulae. Sir W. Her- 
schel, who observed them with a powerful tele- 
scope, speaks of them in these terms : 

" A very remarkable circumstance attending 
the nebulae and clusters of stars is, that they are 
arranged in strata, which seem to run on to a 
great length, and some of them I have been al- 
ready able to pursue so as to guess pretty 
well at their form and direction. It is probable 
enough, that they may surround the whole ap- 
parent sphere of the heavens, not unlike the 
milky-way, which is undoubtedly nothing but a 
stratum of fixed stars. As this latter immense 
starry bed is not of equal breadth or lustre in 
every part, nor runs in one straight direction, 
but is curved and even divided into two streams 
along a very considerable portion of it, we may 
likewise expect the greatest variety in the clus- 
ters of the stars and nebulae. One o'l these nebu- 
lar beds is so rich, that in passing through a sec- 



24 



Arago and Lardner's Astronomy. 



tion of it, only in the time of thirty-six minutes, 
I detected no less than thirty-one nebulas, all 
distinctly visible upon a fine blue sky. Their 
situation and shape, as well as condition, seems 
to denote the greatest variety imaginable. In 
another stratum, or perhaps a different branch 
of the former, I have seen double and treble ne- 
bulas, variously arranged ; large ones with small, 
seeming attendants ; narrow, but much extend- 
ed ; lucid nebulas, or bright dashes ; some of the 
shape of a fan, resembling an electric brush, is- 
suing from a lucid point ; others of the cometic 
shape, with a seeming nucleus in the centre ; or 
like cloudy stars surrounded with an atmo- 
sphere ; a different sort again contain a nebulosity 
of the milky kind, like that wonderful inexplicable 
phenomenon about Orionis ; while others shine 
with a fainter mottled kind of light, which de- 
notes their being resolvable into stars. 

" It is very probable that the great stratum cal- 
led the milky-way, is that cluster in which the 
sun is placed, though perhaps not in the very cen- 
tre of its thickness. We gather this from the ap- 
pearance of the galaxy, which seems to encom- 
pass the whole heavens, as it must certainly do 
if the sun is within the same. For suppose a 
number of stars arranged between two parallel 
planes, indefinitely extended every way, but at 
a given considerable distance from each other ; 
and calling this a sidereal stratum, an eye placed 
somewhere within it will see all the stars in the 
direction of the planes of the stratum projected 
into a great circle, which will appear lucid on 
account of the accumulation of the stars ; while 
the rest of the heavens at the sides will only 
seem to be scattered over with constellations, 
more or less crowded, according to the distance 
of the planes, or number of stars. contained in the 
thickness or sides of the stratum. 

"We are now in a condition to appreciate the 
position occupied by our little planet in this 
vast system. Let us take a star of this immense 
congeries, and compare it with the innumerable 
quantity of the others ; and that we may judge 
the better, let us examine it at first with the 
naked eye. The stars of the first magnitude, 
being in all probability the nearest, will furnish 
us with a step to begin our scale. Setting off 
therefore with the distance of Sirius or Arcturus 
for instance, as unity, we will at present sup- 
pose, that those of the second magnitude are at 
double, and those of the third at treble the dis- 
tance, and so forth. It is not necessary critically 
to examine what quantity of light, or magnitude 
of a star, entitles it to be estimated of such or 
such a proportional distance, as the common 
coarse estimation will answer our present pur- 
pose as well ; taking it then for granted, that a 
star of the seventh magnitude is about seven 
times as far as one of the first, it follows that an 
observer who is inclosed in a globular cluster of 
stars, and not far from the centre, will never be 
able, with the naked eye, to see to the end of it : 
for since he can only extend his view to about 
seven times the distance of Sirius, it cannot be 
expected that his eyes should reach the border 
of the cluster, which has perhaps not less than 
fifty stars in the depth everywhere ai'ound him. 
The whole universe, therefore, will to him be 
comprised in a set of constellations richly orna- 
mented with scattered stars of ail sizes. Or if 



the united brightness of a neighboring cluster of 
stars should in a remarkably clear night reach 
his sight, it will put on the appearance of a small, 
faint, whitish, nebulous cloud, not to be per- 
ceived without the greatest attention. Allow- 
ing him now the use of a common telescope, 
he increases his power of vision, and applying 
himself to a close observation, finds that the 
milky-way is indeed no other than a collection 
of very small stars. He perceives that those ob- 
jects, which had been called nebulas, are evi- 
dently nothing but clusters of stars." 

Herschel remarks that in the most thickly set 
portion of the milky-way, there are fields of 
view, embracing only a few minutes, which con- 
tain as many as 588 stars ; that in a quarter of an 
hour he has seen 116,000 pass through the field 
of his telescope, the opening of which was but 
15' : and that at another time he has seen 258,000 
pass it. Every improvement he made in his tele- 
scopes enabled him to discover still more stars, 
and it does not appear that there are any more 
limits to their number than to the extent of the 
universe. 

Our sun is probably but a fixed star, since if 
it was transported to a distance, within which 
we shall presently demonstrate that the stars 
cannot be situated, it would have absolutely the 
same appearance. What other conclusion can 
be drawn from this but that the stars, which 
shine with their own light, since their distances 
are immeasurable, are comparable to the sun 
in brilliancy and in volume ; that they must be 
as distant from each other as they are from us ; 
and that analogy would show that, like our sun, 
they disperse light and heat to the planetary sys- 
tems that gravitate round them ? 

Herschel thinks that our sun, like the majori- 
ty of the stars, has a direct progressive motion 
toward the constellation of Hercules, in which it 
carries all our planetary system along with it. 
He remarks that the apparent motions of forty- 
four out of fifty-six stars he studied, are nearly 
such as would be produced by a real motion of 
this kind in the solar system, and that the bril- 
liant stars of Sirius and Arcturus, which are 
probably the nearest to us, exhibit, as they 
should do according to the theory, the greatest 
apparent motions. The star Castor appears, 
when viewed by the telescope, to be formed of 
two stars of nearly equal size,* and though they 
have an apparent motion, it has not been possi- 
ble to detect in them a variation of their relative 
distance, amounting to a single second ; a fact 
which it is easy to comprehend, if their appa- 
rent motions are owing only to a real motion in 
the sun. 

On looking over the catalogues of stars left us 
by the ancients, we are struck by a very singu 
lar fact: some of these stars have changed their 
lustre in a manner more or less remarkable ; and 

* This is also the case with the pole-star, and s6me 
others. In viewing these double stars a singular phe- 
nomenon discovers itself, first noticed by Herschel: 
some of them are of different colors, winch, as the ima 
ges are so near each other, cannot arise from any defect 
in the telescope, a Hercnlis is double, the larger star is 
red, the smaller blue : e Lyrce is composed of four stars, 
three white and one red : y Andromeda; is double, ttte lar- 
ger reddisli white, the smaller a fine sky-blue. Some 
single stars evidently differ in their color: Aidebaran is 
red, Sirius brilliant white — [Biiriktey Elem. Astr. . 



Arago and Larmier's Astronomy. 



25 



while some have made their appearance, that 
had never before been seen, oihei-s have disap- 
peared to return again, or in some instances 
without ever reappearing. These astonishing 
phenomena have occurred at all periods. The 
"following is an interesting extract from Halley on 
these extraordinary changes. 

The first new star of Cassiopea " was not seen 
by Cornelius Gemna, on the 8th of November, 
1572, who says, he that night considered that 
part of the heavens in a very serene sky, and 
saw it not, but that the next night, November 9, 
it appeared with a splendor surpassing all the 
fixed stars, and scarce less bright than Venus. 
This was seen by Tycho-Brahe before the 11th 
of the same month, but from thence he assures 
us it gradually decreased, and died away, so that 
in March, 1574. after sixteen months, to be no 
longer visible ; and at this day no signs of it re- 
main. The place thereof in the sphere of fixed 
star-:, by the accurate observations of the same 
Tycho, was s 9° 17' right ascension, with 53° 
45' north latitude. 

" Such another star was seen and observed by 
the scholars of Kepler to begin to appear on 
September 30, 1G04, old style, which was not to 
be seen the day before : but it broke out at 
once with a lustre surpassing that of Jupiter, and 
like the former it died gradually away, and in 
much about the same time disappeared total- 
ly, there remaining no trace thereof in 1605. 
This was near the ecliptic, following the right 
leg of Serpentarius, and by the observations of 
Kepler and others, was in 7s 20° 0' right ascen- 
sion, with north latitude 1° 56'. These two 
seem to be a distinct species from the rest, and 
nothing like them has appeared since. 

" But between them, viz. in the year 1596, we 
have the first account of the wonderful star in 
collo Ceti, seen by David Fabricius, on the 3rd of 
August, old style, as bright as a star of the third 
magnitude, which has been since found to ap- 
pear and disappear periodically ; its period be- 
ing precisely enough seven revolutions in six 
years, though it return not always with the same 
lustre, nor is it ever totally extinguished, but 
may at all times be seen with a six-foot tube. 
This was singular in its kind, till that in collo 
Cygni was discovered. It precedes the first 
star of Aries 1° 40', with 15° 57' south latitude. 

M Another new star was first discovered by 
Will. Jansonius in the year 1600, in pectore or 
rather in eductione colli Cygni, which exceeded 
not the third magnitude. This having contin- 
ued some years, became at length so small, as to 
be thought by some to disappear entirely; but 
in the years 1657-8-9, it again rose to the third 
magnitude, though soon after it decayed by de- 
grees to the fifth or sixth magnitude, and at this 
day is to be seen as such in 9s 18° 38' right as- 
cension, with 55° 29' north latitude. 

" A fifth new star was first seen and observed 
byHevelius, in the year 1670, on July 15, old 
style, as a star of the third magnitude ; but by 
the beginning of October was scarcely to be per- 
ceived by the naked eye. In April following, 
it was again as bright as before, or rather greater 
than of the third magnitude, yet wholly disap- 
peared about the middle of August. The next 
year, in March, 1672, it was again seen, but not 
exceeding the sixth magnitude, since when it 



has been no further visible, though we have fre- 
quently sought for its return: its place is 9s 3° 
17' right ascension, and has north lat. 47° 28'. 

" The sixth and last is that discovered by Mr. 
G. Kirch, in the year 1686, and its period de- 
termined to be 404^ days: though it rarely ex 
ceeds the fifth magnitude, yet it is very regular 
in its returns, as we found in the year 1714. 
Since then we have watched, as the absence of 
the moon and the clearness of the weather would 
permit, to catch the first beginning of its appear- 
ance in a six-foot tube : that bearing a very great 
aperture discovers most minute stars. And on 
June the 15th last, it was first perceived like 
one of the very least telescopical stars ; but in 
the rest of that month, and in July, it gradually 
increased, so as to become in August visible to 
the naked eye, and so it continued all the month 
of September. After that it again died away by 
degrees, and on the 8th of December, at night, 
was scarcely discernible by the tube, and as near 
as could be guessed, equal to what it was at its 
first appearance on June 15 : so that this year it 
has been seen in all near six months, which is but 
little less than half its period, and the middle 
and consequently the greatest brightness falls 
about the 10th of September." 

Two classes have been formed of the stftrs, 
supposed in the last century to be variable. In 
the first are those which are certainly so, in the 
second those which are only supposed to be so. 
The first are twelve in number, from the first to 
the fourth magnitude, including that which ap- 
peared in Cassiopea, in 1572, and that which was 
seen in 1604, in Serpentarius. The second class 
contains thirty, from the first to the seventh mag- 
nitude. 

Conjecture has been exhausted to account for 
these surprising changes. Newton thought that 
the transient vivacity of their lustre was owing 
to an increase of combustible matter, produced 
by the fall of a comet. This system of Newton's, 
which would have it that comets are intended to 
feed the combustion of the stars, precisely in the 
same way as so many pieces of fuel which we 
throw into the fire, is but little in harmony with 
the means employed by nature, and with the 
probable mode of combustion of the celestial 
bodies, which can hardly be owing to any other 
than electrical agency. Maupertuis supposes 
that the stars have such a rapid rotary motion, 
that the centrifugal force must have given them 
the figure of a spheroid so greatly flattened as to 
be reduced to a circular plane like a mill-stone; 
and that in this way they necessarily appear to 
us very brilliant, when their motions so incline 
them that they present to us the faces of their 
disks, while on the other hand they are hardly, 
or not at all, visible to us when their edges alone 
are turned toward us. Others have thought 
that these changes were produced by dark spots 
spread over the surface of the stars, or else that 
these bodies revolve in orbits so vast, that, like 
the comets, they are only visible when in the 
points of their orbits the nearest to us. The 
more probable opinion respecting these periodic 
stars is, that they have a dark face. 

These observations suggest a reflection. Our 
sun, we have said, is a star. Has it never under- 
gone analogous variations .' and if it has experi- 
enced some of these great vicissitudes, what pro- 



26 



Arago and Lardner's Astronomy. 



digicras consequences mtist have resulted from 
thetn ? These considerations are perhaps de- 
serving of the serious attention of geologists, in 
their search after the causes of those tremendous 
catastrophes, of which our globe everywhere 
affords traces. 

To close the subject of this lecture it now re- 
mains for us to form, if possible, an idea of the 
distance that separates us from the fixed stars. 
Before engaging in this problem, we shall lay 
down some indispensable preliminaries. 

The angle subtended by an object varies in- 
versely as the distance of the object from the 
spectator's eye. This is one of the most ele< 
rnentary propositions in geometry. 

Again, trigonometry makes known the rela- 
tions that exist between the dimensions of a 
body, its distance, and the angle it subtends : 
thus an object which subtends an angle of 1° is 
at 57.38 times its dimensions; if the angle it 
subtends is 1', it is at 3436 times its dimensions, 
and 206,000 times if the angle subtended is 1". 

This being established, it is easy to conceive 
that, the diameter of the earth being known, if 
we knew the angle it subtends when viewed 
from the stars, we should thereby at once have 
the distance of these stars. This angle is what 
is called the parallax. To find it we employ a 
method similar to that had recourse to for find- 
ing the distance between terrestrial objects. It 
consists in taking a base of a known length, and 
measuring the angles formed with it at its ex- 
tremities by the visual rays proceeding from the 
object whose distance is recpiired. These an- 
gles being measured, their sum i3 subtracted 
from 180° ; the remainder is the angle sought, 
according to the very pregnant proposition of ge- 
ometry, that the three angles of a triangle are 
always equal to two right angles. 

But when we proceed in this way, taking for 
our base the radius or diameter of the earth, the 
parallax it gives is not appreciable in relation to 
the stars ; which shows that the diameter of the 
earth is a quality altogether imperceptible, when 
compared with the distance that separates us 
from the fixed stars. 

Since three thousand leagues are nothing com- 
pared to the distance of the fixed stars, to what 
standard of comparison shall we have recourse 
to measure the latter ? To one which, perhaps, 
will suffice — the great diameter cf the terrestrial 
orbit, a length of 190,000,000 miles. This is 
what is called the great parallax, or the annual 
parallax. Hook, Flamsteed, and Bradley, ob- 
served with the zenith sector, at the vernal and 
autumnal equinoxes, the passage of y Draconis 
across the perpendicular wire, expecting that 
the diameter of the earth's orbit would show 
an angle or parallax with it. Their expecta- 
tion was not realized ; the angle was not appre- 
ciable. And vet, if the annual parallax of these 
etars was only one second, they would still 
be more than 14,000,000,000,000 miles from us, 
and we might measure their volumes. Can any- 
thing more strikingly impress us with ideas of 
the immensity of space, especially if we reflect 
that these millions of stars strewed before our 
eyes, are all at immeasurable distances from each 
other ! 

* By observations made within the last few 
fears, it has been ascertained that some of the 



j amounting to auoui si. 
I the length of that line. 
I sun and earth measure 



nearest stars have a parallax amounting to about 
one-third of a second. An object at which the 
line joining the sun and earth would subtend an 
angle of that magnitude, must be at a distance 
amounting to about six hundred thousand times 
e. But the line joining the 
es about one hundred mil- 
lions of miles in length ; consequently, the dis- 

j tance of the nearest stars must be about sixty 
millions of millions of miles. The gradually 
decreasing brightness of the stars of various or- 
ders being known to arise, not from any intrin- 
sic difference of brightness, but merely from 
their difference of distance from us, Sir W. Her- 
schel observed, by comparing theirrelative splen- 
dor, that the smallest stars visible to the naked 
eye, may be safely inferred to be twelve times 
more distant than the nearest and brightest. 
They must, consequently, be at the distance of 
seven hundred and twenty millions of millions 
of miles. But again : the telescope discloses 
various orders of stars still more distant ; magni- 
tudes decreasing from the eighth to the sixteenth 
are rendered visible by it. They are therefore 
placed at still more prodigious distances. The 
smallest star visible in his forty foot telescope, 

| was estimated to be two hundred times more 
distant than the smallest star visible to the naked 
eye. The distance of such a star must then be 
one hundred and forty-four thousand millions of 
millions of miles. 

* The mind is lost — the imagination over- 
whelmed by such spaces. We have no standard 
commensurate with them, nor any familiar 
means of clearing our conception of them. As- 
tronomers themselves, accustomed as they are to 
the contemplation of vast magnitudes, distances, 
and numbers, have been compelled to resort to 
unusual expedients to express the distances of 
the stars. 

* Light, the swiftest known physical principle, 
j has been ascertained to be propagated through 

space with a velocity amounting to two hundred 
thousand miles per second ; that is to say, it pass- 
es over that space between two ticks of a com- 
! mon clock. Thus a fire suddenly lighted at the 
distance of twenty thousand miles, would be 
visible after the lapse of one-tenth of a second. 
If lighted at the distance of two millions of miles, 
it would not be visible until after the lapse of 
ten seconds, and so on. The sun is not actually 
seen until about eight minutes after it rises, be- 
cause, being at a distance of one hundred mil 
lions of miles, light takes five hundred second*, 
to arrive from it at the eye, and mftil the light 
does arrive, the object cannot be seen. 

* Now the nearest stars being sixty millions of 
millions of miles from us, their light will take 
three hundred millions of seconds to come from 

jj them to us, or about ten years to arrive at our 
|< globe. The light of those which the naked eye 
jj can barely discern, would take one hundred and 
!j twenty years to come to us ; and the light of the 
Ij smallest telescopic stars would require twenty- 
' four thousand years to make its passage. The 
i contemplation of the heavens on a clear night, 
; offers, then, a strange history of the past. We 
i behold the Dog star ; yet that star may have 
i ceased to exist nine yeai*s and eleven months and 
j three weeks ago ! The smallest stars we see 
, twinkle in the firmament, are bodies which ex- 



Arago and Lardner's Astronomy. 



27 



isted a hundred and twenty years ago, but of 
whose existence now we cannot be sure for a 
hundred and twenty years to come. 

* But vast as these distances are, and strange 
as the consequences of these natural laws may 
seem, they are less surprising than others which 
modern discovery has unfolded. The telescope 
has made known the existence of masses of stars, 
the distances of which are so great that they ap- 
pear to our telescopes as a mere spot of light ; 
yet the individual stars composing such masses 



are separated by distances analogous to those 
which separate our smi from the fixed stars ! It 
has been conjectured, with great probability, 
that the distances of these bodies must be such, 
that light would take several millions of years 
to move through it ! 

* The following diagrams from Gale's Natural 
Philosophy, will illustrate the preceding obser- 
vations. The first (Figure 20,) represents a com- 
pressed cluster of stars, the centre part 8' 
long, 2'broad: 




The following (Figure 21,) represents another similar cluster of stars 




In February, 1814, Dr. Herschel read to the 
Royal Society, the results of thirty years' ob- 
servations on nebulae, with the best telescopes 
ever possessed by man. He conceives that 
the stars form independent systems of them- 
selves. He considers our sun as part of that 
shoal or system which we call the milky-way, 
and that all the stars of the first, second, and 
third magnitude, belong to that vast cluster. 
The stars, he remarks, are not spread in equal 
portions over the celestial sphere, but are found 
in patches, each containing many thousands, 
and many more than the eye can separate 
from the mass. These he calls Clusters ; and 
he conceives that they have a constant dis- 
position to unite more, by a power which he 
calls the Clustering Power. He gives an ac- 
count of eighty of these clusters, some of the 
drawings of which are copied on this and pre- 
ceding pages 



The following figure represents a globular 
cluster 2' in diameter, as seen with Herschel's 
40 feet telescope : 




28 



Arago and Lardner's Astronomy. 



LECTURE V. 

DISTANCES OF THE PLANETS.— THE SUN.— THE MOON, 



DISTANCES OF THE PLANETS. 

However great the magnifying power of the 
instrument we employ, the apparent diameter 
of the fixed stai's is never changed. The planets, 
on the contrary, exhibit disks, whose diameters 
increase with the power of the instrument with 
which we observe them. This difference pre- 
sents us at once with a convincing proof, that 
they are much nearer to us than the fixed stars ; 
and the micrometer proves that this distance 
varies, since it exhibits variations in their appa- 
rent diameters. 

The moon, whose distance from the earth ob- 
servations of this kind prove to be necessarily 
very small, was early subjected to the investi- 
gations of modern geometry. MM. Lacaille 
and Lalande, betook themselves, the one to Ber- 
lin, the other to the Cape of Good Hope, to de- 
termine the moon's parallax. We have already 
explained this terra as signifying the angle con- 
tained between two visual rays proceeding from 
a star to each extremity of the earth's radius. 
They found this angle (for the centre of the 
moon's disk) to be 1°, which gives for the moon's 
mean distance from the earth about sixty ter- 
restrial radii, or 80,000 leagues (230,000 miles). 
The moon's diameter is about one-fourth that of 
the earth, and its bulk about the fiftieth,part of 
the latter's. 

The possible amount of error in this method 
of computing the distance, may be half a sec- 
ond for each of the angles measured at Berlin 
and at the Cape, consequently one second for 
the entire result ; that is to say, the 3600th part j 
of the distance. The method must always be 
subject to this amount of error, because we can- 
not be sure of an angle within less than half a 
second. 

The sun's parallax is 8".6 to ~~, and its mean 
distance is 34,000,000 leagues (94^ millions of 
miles). Its diameter is to that of the earth, in 
the proportion of 111 to 1, and its bulk in the 
proportion of 1,300,000 to 1. 

The sun's parallax is known within a tenth of | 
a second, a much closer approximation than w r e j 
have been able to obtain by the ordinary method, 
having been made by another which we shall jl 
explain. 

It is furnished by the transits of Venus across 
the sun's disk. Let S be the sun, AB the earth's 
radius, and vv' Venus, describing her orbit round 
the sun. Let us now suppose that two observ- 
ers placed, the one at A, the other at B, observe 
and accurately note the different phases of the 
conjunction; the difference of their results will 
give the time occupied by Venus in passing 
over the circular arc vv', which arc is itself the 
measure of the sun's parallax. This operation, 
which we here present in so simple a form, is 
rendered complicated by the motions of the 
earth, and other particulars, for which it is neces- 
sary to make due allowance, in order to obtain 
a result entirely divested of error. 



Fis. 23 




The distances and volumes of the other plan 
ets have been determined by similar means : we 
shall give the results when we come to speak 
of them in detail. We may pause, however, to 
remark the singular numerical relations existing 
between the distances of the planets from each 
other. If we take the following numbers, 0, 3, 
6, 12, 24, 48, 96, 192, and then add to each of 
them the number 4, we shall have 4, 7, 10, 16, 
28, 52, 100, 196, expressing the order and propor- 
tion of the planets' distances from the sun, thus 
0.3. 6 . 12 . 24 . 48 . 96 . 192 
4 7 10 16 28 52 100 196 

2 ..? # j ■'■£ ■ % :.h JS 

Kelper, considering these relations, and, observ 
ing in them a void between 16 and 52, ventured 
to predict the discovery of the new planets, and 
it was this conjecture that guided the investiga- 
tions of the astronomex-s who discovered them. 



We have just seen that the sun is an immense 
globe, 1,300,000 times greater than the earth, 
and that its mean distance from us is 34,000,000 
leagues (94^ millions of miles). We shall see, 
by and by, how gravity supplies us with the 
means of determining its density and its weight, 

We have already said, on the authority of 
Herschel, that this star is probably carried, with 
all its train of planets, toward the constellation 
of Hercules : it has, moreover, a motion of rota- 
tion upon its own axis, which it accomplishes 
in 25 £ days. This is proved by observing the 
spots on its surface. The manner in which 
these spots move, and the various aspects they 
assume, according as they present themselves to 
us obliquely or with their faces toward us, leave 
no manner of doubt that they are inherent in 
the surface of the sun, and that this star is «l 
spherical body. We omit, for the present, its 
apparent motion in the plane of the ecliptic : 
further on we shall see it is the result of the 
transference of the earth to the different points 
of its orbit. 



Araso and Lardner's Astronomy. 



29 



PHYSICAL CONSTITUTION OF THE SUN. 

The sun, we have said, exhibits spots on its 
surface ; some of these are obscure, others lu- 
minous ; the latter have acquired the name of 
/acuta;. Their form is very irregular, their du- 
ration very variable, and they are commonly sur- 
rounded by a penumbra. They are always com- 
prised within a zone, whose extent varies north 
and south of the solar equator. 

Many conjectures have been offered in expla- 
nation of these spots. Some have supposed that 
the sun, from which so vast a quantity of light 
and heat is incessantly emanating, is a body in a 
state of combustion, and that the dark spots are 
nothing else than scorias floating on its surface. 
The faculae, on the contrary, they suppose due 
to volcanic eruptions from the liquified mass. 
The grand objection to this hypothesis is, that it 
does not suffice to explain the phenomena: it 
has not obtained admission among astronomers. 
The opinion most in favor in the present day, 
regards the sun as consisting of an obscure and 
solid nucleus, enveloped by two atmospheres — 
the one obscure, the other luminous. In this 
view of the case, the appearance of the spot is 
explained by ruptures occurring in the atmo- 
sphere, and exposing the globe of the sun to 
view. The penumbra is the extremity of the 
inner and dark atmosphere, the rent in which is 
not so wide as in the luminous one, and which 
is seen round the opeuing that exposes the cen- 
tral nucleus. 

This opinion, however strange it may appear, 
has the advantage of perfectly explaining all the 
phenomena, and it acquires a high degree of 
probability from the consideration, that the in- 
candescent substance of the sun cannot be either 
a solid or a liquid, but necessarily a gas. 

It is an established fact that rays of light, issu- 
ing from a solid or liquid sphere in a state of in- 
candescence, possess the properties of polariza- 
tion, while those emanating from incandescent 
gases are devoid of them. From the application 
of this principle, to experiments made on solar 
light, has been derived the conclusion we have 
already stated. 

These experiments are made by means of a 
very ingenious instrument, the principle of 
whose construction is founded on the properties 
of polarized light. It is a telescope furnished 
with a piece of crystal, and presenting ia its fo- 
cus, when we look at the sun, two colored im- 
ages. A very simple mechanism enables us to 
cause the one or the other of these images to re- 
cede or advance, or even to cause one of them 
to cover the other wholly or partially. This 
telescope affords proof that the light of the sun's 
edges is as intense as that of its centre. For, if 
the two images of the sun be made to lap over 
each other, so that the edge of the one may be 
upon the centre of the other, perfectly white 
light will be produced at the points of coin- 
cidence. Hence it follows, 1. That the edges of 
the sun possess a light as intense as the centre: 
2. That the colors of the two images, produced 
by the telescope, are complementary the one of 
the other. 

But from the fact that the light from the edges 
of the sun's disk is as intense as that from the 
centre, there follows another consequence ; 



namely, that the sun has no other atmosphere 
outside the luminous one; for, otherwise the 
light of the edges, having a deeper layer to pene- 
trate, would be found more weakened. 

What is the nature of the light we derive from 
the sun? This question has long divided natu- 
ral philosophers. Some, supported by the au- 
thority of Newton, maintained that the sun, as 
well as all luminous bodies, has the property of 
discharging exceedingly minute particles of its 
substance with prodigious velocity: this is the 
theory of emission, or the corpuscular theory. 
Others, on the contrary, supposed that the phe- 
nomenon of light is produced by the vibrations 
of a fluid called ether, diffused through all na- 
ture, and set in motion by the presence of lu- 
minous bodies: this is the theory of vibrations, 
or the undulatory theory. It is now-a-days uni- 
versally received ; for it is impossible to conceive 
how a body should incessantly discharge por- 
tions of its substance without losing anything of 
its bulk and brilliancy. But the greatest defect 
of the theory of emission, is, that it does not in 
the present day satisfy all the conditions, where- 
as the other combines in its favor every proba- 
bility, especially since recent discoveries have 
manifested evidence of the most intimate rela- 
tions between the cause that produces electrical 
phenomena, and that which gives origin to 
light. 

M. Pouillet proposed to himself the problem 
of determining the temperature of the sun's rays. 
Let us imagine, he says, a sphere of ice with an 
opening which will admit of a thermometer be- 
ing inserted, and reaching its centre, where it 
will maintain itself at a temperature of (Reau- 
mur.) Now, suppose we cause rays of light to 
fall on the thermometer, it will acquire warmth, 
and will rise a certain quantity. Now, if we 
know the distance from the luminous body to 
the thermometer, the proportion the opening by 
which the rays of light have had admission bears 
to the circumference of the sphere, and the 
quantity by which the thermometer has risen, 
we can calculate the quantity of heat sent to the 
instrument by the incandescent body. Thus, 
whatever be the distance, provided it be known, 
it will always be easy to come at the quantity of 
heat supplied by means of the thermometer. 

M. Pouillet found by this method, that his 
thermometer, placed under the circumstances 
described, never rose more than seven degrees 
and a half, and never fell lower than six de- 
grees, which gave him a mean temperature of 
about 1200 degrees for the solar rays. 

Lastly, it has been asked, whether the rays of 
light — whose velocity is enormous, since, as we 
shall show, it exceeds 70,000 leagues in a sec 
ond — have any appreciable impulsive force: but 
the most delicate experiments have detected 
nothing of the kind. 

* That the spots on the sun are cavities in a 
luminous coating, is proved by observations. 
When the part of the sun on which one of these 
spots is situate, is first brought into view by the 
rotation of the sun on its axis, the spot itself is 
not visible, which it would be, were the spots a 
black patch on the surface of the sun. But, be- 
ing an excavation, the bottom does not become 
visible until it comes round to a direction more 
fronting the line of. vision. 



30 



Ar ago and Lardner's Astronomy. 



of the excavation in the first instance, intercept 
the view of the bottom. 

* That the sun is a globe composed of non- 
luminous matter, covered with a laminous coat- 
ing of considerable thickness, may be considered 
to be established as certainly as any other physi- 
cal truth. But what is the nature of that lu- 
minous matter ? and what is the origin of those 
inexhaustible stores of light and wannth which 
it supplies? These are questions not so cer- 
tainly or clearly answered. The reporter of 
M. Arago's lectures, has represented that as- 
tronomer as stating that the luminous coating of I 
the sun must be matter in a gaseous state, and 
assigning the following demonstration as a proof 
of this: Modern discoveries respecting light) 
have established the fact, that physical principle 
may exist in two distinct states, one of which j 
has been called the ordinary state of light, and] 
the other the polarized state. M. Arago is rep- j 
resented as stating, that the light proceeding! 
from incandescent bodies, either in the solid or j 
liquid state, is always polarized, while that 
which proceeds from a body in the gaseous || 
state, or in other words, from flame, is always 
in its ordinary or uupolarized state ; or to use 
the more exact terms of the reporter, the light 
of the former possesses the properties of polari- 
zation, while that of the latter does not. The 
light proceeding directly from the sun, being || 
ordinary and not polarized light, the condition j 
of the matter from which it issues, must be j 
gaseous. We have been unable to refer to any j 
original researches on these points, and can only 
leave the statements of the reporter as they 
stand. 

"It had long been a received opinion that the 
sun was enveloped in an atmosphere outside its j 
luminous coating, as that of the earth is outside 
its solid crust; if such were the case, the partial; 
opacity of such a gaseous envelope would cause 
the centre of the sun's disk to appear brighter j 
than the borders, the former being seen through j 
a less thickness of the atmosphere. The testj 
referred to by M. Arago, of the double image 
produced by certain crystals, clearly decided 
this question, and proved that the light on every 
part of the sun's disk is uniform, and as a conse- 
quence, that there is no atmosphere outside the 
luminous coating. 

* The nature of light in general, has much en- 
gaged the attention of philosophers, from the j 
time of Galileo to the present day. Two, and \ 
only two explanations have been or can be ap- j 
plied to it; the one countenanced by Newton j 
and his immediate successors in the English! 
school, is the corpuscular theory; the other ad- 
vanced by Huygens, and generally adopted by 
continental philosophers, has been called the un- 
dulatory theory. In the former, light is contem- 
plated as a form of matter, sui generis ; its par- 
ticles or molecules are supposed to be ejected 
or emitted continually from all visible bodies, 
and to enter the pupil of the eye, to stimulate 
the retina by their impulse upon it, and thereby 
produce vision. In the undulatory theory on 
the other hand, light is considered to be a phe- 
nomenon in all respects similar to sound, and ! 
the eye to be an organ analogous to the ear. J 
To the completeness of such a theory, the sup- 
position of a medium for the transmission of the 



undulations, is indispensable, which medium 
must discharge the same functions in regard to 
light, as the atmosphere discharges in regard to 
sound. The existence of such a medium is ac- 
cordingly assumed in the undulatory theory, and 
has been called the luminiferous ether; it is 
supposed to pervade the universe, filling all the 
space between planet and planet, and star and 
star. It is the messenger of light, as air is the 
messenger of sound. For a iong period this 
universal atmosphere was a mere hypothetical 
medium, adopted because it was necessary 
to the undulating theory. No direct proof of 
the existence of such a medium had been ob- 
tained. Within a late period, however, indica- 
tions of its reality have been obtained from the 
movements of some of the periodic comets. 
Encke's comet was the first body which be- 
trayed its presence; it was ascertained in its 
successive revolutions round the sun, to have a 
gradually diminishing period, and consequently 
a gradually diminishing orbit. This was an 
effect which would immediately follow from a 
slightly resisting medium, and which could be 
explained by no other cause. The comet of 
Beila, another periodic body of that class, has 
afforded similar indications. , 

* The undulating theory has, for the last half 
century, been gradually augmenting the number 
and authority of its partisans, while the ranks 
of the corpuscular hypothesis have been so 
thinned, that few of any eminence remain in 
them — while the undulatory theory affords a 
satisfactory explanation of all, or nearly all the 
phenomena which observation has developed, 
and has enabled us by the due application of 
mathematical science to predict unobserved, 
and produce unlooked-for effects, the failure 
of the corpuscular theory has been more and 
more frequent, as the limits of experimental 
inquiry have been more and more widely ex- 
tended. The undulatory theory may, in fact, 
now be regarded as generally admitted. 

The Moon J) . 

The moon, we have seen, is but the fiftieth 
part of the bulk of the earth, and its distance is 
but 80,000 leagues, or 230,000 miles; so that with 
an instrument which magnifies one thousand 
times, we can see her as she would appear to 
the naked eye if she were only 230 miles off. 

The moon's motions are very complicated, 
and for a long time greatly embarrassed astrono- 
mers. She moves in an ellipsis, of which the 
earth occupies one of the foci, and which she 
describes in twenty-nine days, twelve hours, 
forty-four minutes, two seconds. She is at the 
same time earned along by the earth in its revo- 
lution round the sun; and while the latter occu- 
pies a year in its revolution, the moon has 
already traversed her own orbit thirteen times 
and a half. She turns upon her axis precisely 
in the same time as she takes to revolve round 
the earth; this is the reason why she always 
presents to us the same face. 

From the combined effects of these motions 
result the moon's phases, that is to say. ihe dif- 
ferent aspects under which we see this planet 
at different periods of her course. Thus let S 
be the sun, and T the earth, and let us vre what 
will be the appearance of the moon. When it 



Arago and Lardner's Astronomy. 



31 



Fig. 24. 





is at A in conjunction with the sun, it will pre- 
sent to the earth its unilluminated half. Arrived 
;it B, after having described the eighth part of 
its orbit from the conjunction, it will present to 
ihe earth the fourth of its illuminated portion, 
and wiil be seen under the aspect it wears at b. 
At C it will have described the fourth part of 
its orbit, and will exhibit half its enlightened 
part, as at c. At D it will show more than half 
its i [laminated side, as at d, and it will show it 
completely at E, as represented at e. Setting 
out from E it will begin to wane, and will pre- 
sent the same phenomena, but in an invei-se or- 
der, as shown in the figure, where the interior 
circle exhibits the moon as it would appear to a 
spectator placed on the sun, and the exterior 
circle as it is seen from the earth. 

Such are the different phases which the moon 
describes in the space of twenty-nine days and 
a half. When full, that is, when she presents 
the entire of her illuminated disk to the earth, 
Hhe is said to be in opposition to the sun; when 
the moon is new, that is, when she presents her 
obscure portion to the earth, and is consequently 
invisible, she is said to be in conjunction', these 
two positions are called syzygies. It is in these 
positions that eclipses of the sun and moon oc- 
cur, as we shall see by and by. Lastly, the moon 
is in her first or her last quarter, when she 
shows us half her illuminated portion, and these 
positions are called quadratures, and the inter- 
mediate points between them and the syzygies 
are called octants. 

The moon's motion is much more rapid than 
that of the sun. In fact, the latter advances but 
a degree a day, while the moon's velocity is 
about thirteen times as great, whence her return 
to the meridian is every day retarded 48' 46''. 
To the difference in the velocity of these two 
motions is owing the return of the conjunction 
after twenty-nine days and a half. 

The plane of the moon's orbit is inclined to 
that of the ecliptic at an angle measuring in the 
mean 5° 8' 49'': the points of intersection of 
ihese planes are called nodes, the one ascending 
>!_, that from which the moon rises toward the 
boreal pole; the other descending "\5> tnat from 
which it sinks toward the austral pole. 

A fact that admits of no question, and that 
rests upon the most exact observation, proves 
that the moon's nodes move toward the west, 



and thus travel round the ecliptic in a direction 
contrary to the apparent course of the sun, or in 
the direction of the diurnal motion from east to 
west. Every year they complete about. 19£°, 
which makes 1° every 19 days, or 1° 28' every 
periodical lunar month, or lastly, an entire revo- 
lution of the heavens every eighteen years and 
a half: more exactly, the nodes retrograde 19° 
•3286 annually, and complete their revolution of 
the ecliptic in 6788-54019 days. We find also 
that the synodic revolution of the node takes 
|j place in 346-61963 days, that is to say, that after 
1 1 this interval the sun is situated again in the 
moon's node. As the sun moves in a contrary 
direction to the node, they meet a little before 
the sun has completed an entire circuit of the 
heavens: this is the reason why this period is 
less than the year. 

We have said that the rotary motion of the 
moon taking place within the same space of 
time as its revolution round the earth, it must, 
as it really does, always present to us the same 
face. We notice, however, from the observa- 
tion of spots on its surface, that it sometimes 
shows us a little more, sometimes a little less, 
of one side or the other, as if it had a slight 
swaying motion like a balance. This is called 
the moon's Ubralion, an expression that very 
well accords with the appearances observed, 
but which yet must not be understood in a 
strictly literal sense, for this apparent oscillation 
is but the effect of an optical illusion. 

The moon's motion in her orbit varies as she 
approaches toward or recedes from the earth, 
while her motion of rotation is always uniform. 
Hence it follows, that during the period of ac- 
celeration, she shows on the east some parts of 
her surface not previously seen, while corres- 
ponding parts disappear on the west: the con- 
verse of this takes place during retardation. 
This is the phenomenon of lib rat ion in longitude. 

Libration in latitude is the consequence of the 
moon's axis of rotation being inclined to her or- 
bit, and of its always preserving its parallelism, 
whence it follows that the moon turns each of 
its poles to us alternately, and displays to us the 
spots situated about it. 

Lastly, the diurnal libration of the moon v\ ill 
be understood upon considering, that though 
the moon constantly turns the same hemisphere 
toward the centre of the earth, u v Ppeetutor, 



32 



Arago and Lardners Astronomy. 



who is removed from that point by the length 
of the earth's radius, perceives, when the moon 
is on the horizon, some parts the mere of one 
side, and a corresponding portion the less of the 
other side. 

PHYSICAL CONSTITUTION OF THE MOON. 

The moon's phases have shown us that she is 
not like the sun,'a self luminous body, but that 
she is opaque, and shines by a borrowed light. 
As for the feeble lustre observable on her unil- 
luminated portion, it arises from the light re- 
flected upon her by the earth, and is called in 
French la lumiere cendree (the ashy light.) 

When we observe the moon's disk with the 
naked eye, we observe on it a multitude of irreg- 
ularities ; but on examining it with a strong tele- 
scope, we observe on the part which is not yet 
illuminated by the sun during the first stages of 
its course, a great number of luminous points, 
which enlarge in proportion as the sun bears 
more directly on the part they occupy. Behind | 
these points a deep shade is projected, which 
turns so as always to be in opposition to the sun. 
These brilliant points are the summits of high 
mountains, which receive the sun's rays before 
the less elevated parts, and the obscure parts on 
which the shadows fall are cavities and valleys, 
which almost in every instance effect the form of 
craters. Geometry affords us the means of mea- 
suring the height of these mountains ; they are 
very elevated for the moon, but less so than 
the peaks of Himalaya. The shadows they 
project enable us to measure their elevation as 
well as the depth of the valleys ; it is also to the 
presence of these asperities that we must attrib- 
ute the jagged and irregular appearance occa- 
sionally presented by the moon's disk, the sun 
irradiating their summits, before his rays reach 
their bases. 

The moon has no atmosphere, or at least if it 
has one, it is so rare that it does not differ suffi- 
ciently from a vacuum to cause any refraction of 
light. This is demonstrated by the immersion of 
stars : the latter in fact remain invisible, exactly 
the time they should do, which would not be 
the case if the moon had an atmosphere to re- 
fract the rays of light proceeding to us from these 
stars. 

The axis of the moon being almost perpendic- 
ular to the ecliptic, the sun never sensibly quits 
its equator : it follows from this, that the moon 
enjoys no variety of seasons. But as it turns on 
its axis only once during its period of revolution, 
each of its days and each of its nights is equal to 
fifteen times twenty-four of our hours; and 
what is very remarkable, one of its hemispheres 
is lighted by our earth in the absence of the sun, 
and has no night, while the other has one of fif- 
teen days' duration. 

La Grange endeavored to explain the reason 
why the moon's rotation and her revolution are 
isochronous. He supposed — and he extended 
this supposition to all the other satellites — that 
the face of the moon which is turned toward 
us is very much elongated in comparison with 
the other, and that it is the excess of its weight 
that makes it always turn toward the earth, in 
obedience to the attraction exercised by the 
latter. 

The earth must appear to the inhabitants of 



the moon thirteen times greater than the moon 
does to us. It must present to them very regu- 
lar phases, as will appear from inspection of fig- 
ure 24 ; and always invisible to one half of the 
moon, it is continually seen from the middle of 
the other half. 

While the earth turns on its axis, the aspect 
it presents to the moon must be very various. 
Our seas, continents, forests^ and islands, must 
appear as so many spots of different size and 
brilliancy, and the atmosphere with its clouds, 
must farther modify these appearances in end- 
less variety. 

We have already said that the sun is constantly 
in the moon's equator ; from this it results that 
the inhabitants of this satellite have not the 
same means as we of computing time ; in fact, 
we measure the year by the return of the equi- 
noxes, and their cla}^ are always equal. Still 
they might measure it by observing our poles, 
which they see perfectly well, and one of which 
always begins to be enlightened, and the other 
to disappear, as often as the equinoxes return. ' 

Endeavors too have been made to ascertain 
what are the properties of the rays which reach 
us from the moon ; but the most delicate experi 
ments have failed in detecting in this light either 
calorific or chemical properties. Though con- 
centrated in the focus of the largest mirrors, it 
produces no sensible heating effect. To make 
this experiment, recourse has been had to a 
bent tube, the extremities of which terminate 
in two hollow globes filled with air, the one 
transparent, the other blackened, the middle 
space being occupied by a colored fluid. In 
this instrument, when caloric is absorbed by it, 
the black ball takes up more than the other, and 
the air it incloses increasing in elasticity, the 
liquid is driven out. This instrument is so deli- 
cate that it indicates even the 500th of a degree, 
and yet in the experiment alluded to it gave no 
result. The light reflected by the moon has 
therefore no sensible calorific properties. It has 
likewise been ascertained that it has no chemi- 
cal properties ; hydrochlorate of silver, a sub- 
stance that blackens instantly under the influ- 
ence of solar light, has been exposed to the 
moon's rays without undergoing any change. 

Credulity, however, has attributed to the light 
of the moon a great influence over agricultural 
produce, and " la lune rousse" still enjoys a dis- 
mal renown in our rural districts. It is it, they 
say, that freezes the still tender shoots, and ex 
ercises so fatal an influence over the whole 
range of vegetation. It is easy to acquit the 
moon of these misdeeds, of which she is indeed 
quite innocent. What in fact is this same red 
moon? It is that which begins in April and 
ends in May ; that is, at a season of the year 
when the temperature is often four, five, or six 
degrees above (R-). Now we know that 
plants lose by radiation at night a part of the 
heat they have received during the day, and ex- 
perience has shown that this loss may amount 
to seven or eight degrees, when the weather is 
clear, that is, when there are no clouds to neu- 
tralize this radiation ; for the clouds reciprocally 
radiate toward the earth, and serve besides the f 
office of screens, to stop caloric, and prevent its 
dispersion into the higher regions of the atmo- 
sphere. The temperature of plants, which by 



Arago and Lardner's Astronomy. 



33 



day was but four or five degrees, may thus by 
radiation fall several degrees below zero, and 
then the plants will freeze. But., as the exces- 
sive radiation can only take place when the sky 
is unobstructed, and when the moon consequent- 
ly is visible, the influence of this planet will 
have the credit of that which is but a regular 
effect of the variation of temperature. And as 
if everything must concnr to favor this delusion, 
it will be confirmed by the success of the pre- 
cautions supposed to betaken against the malig- 
nant influence of the moon, precautions whose 
real merit is, that they resist radiation. Thus 
gardeners, to protect the young shoots from the 
red moon, cover them with straw or other mat- 
ters, which, forming a screen, hinder, as on 
other occasions do the clouds, the process of ra- 
diation, and thus preserve the plants from the 
frost. 

These accusations against the moon are not 
of modern origin : similar ones were already ad- 
duced by the ancients, and Plutarch asserts that 
its light putrefies animal substances. It is very 
true that, if we place in an exposed situation 
two pieces of meat, and one of them be sub- 
jected to the moon's rays, while the other is pro- 
tected from them by a screen or cover, the for- 
mer will be tainted with putrefaction much 
sooner than the other ; but, in this case, as in 
the former, an effect is attributed to the moon 
that does not emanate from her, and with which 
her rays have nothing whatever to do. That 
the uncovered piece of meat putrefies sooner 
than the other is owing to the fact, that being 
cooled more by radiation, it imbibes a greater 
quantity of moisture; and that moisture is a 
source of decomposition to animal bodies, since 
we dry them to preserve them. 

Another error no less ancient, and no less 
generally diffused, is that which attributes to 
the moon's phases, and to her passages through 
the different quarters, an influence on the varia- 
tions of the atmosphere and the changes of the 
■weather. This popular error, which we find 
supported by the most ancient authors, has no 
foundation. For, not to mention that we cannot 
see how the moon could be instrumental in pro- 
ducing such results, the most exact observations, 
made upon the most extensive and continuous 
scale, formally contradict this supposition. 
Changes of weather are not more frequent at 
the moon's quarterings than at any other period ; 
on the contrary, if there be a difference, scarcely 
perceptible it is true, it is in favor of the octants. 

What then can be the cause of an error so 
long accredited ? Probably the absence of impar- 
tial observations, and the involuntary tendency 
of the human mind to take account only of facts 
favorable to its preconceived opinions, without 
any regard to those that are hostile to them. 
Thus, let a change of weather occur at the re- 
newal of a quarter, one is struck by the coinci- 
dence, one dwells upon it, and leaves unnoticed 
twenty other changes of the moon unaccompa- 
nied by any variation in the atmosphere. 

The authority of Theophrastus has been cited 
in support of the opinion we are combating, an 
authority, be it said in passing, of no great weight 
in matters of science. But those who cite the 
passage in question should have remarked that 
it involves a self-contradiction. For what says 

3 



Theophrastus ! That the new moon brings bad 
weather, the full moon fine, and that the wea- 
ther changes at each quarter. So then, if the 
weather is bad at the new moon, it will be fine 
at the second quarter, consequently bad at the 
full moon, which is in contradiction with the 
words of the passage. 

A modern writer, who published a book in- 
tended to defend popular opinions, has endeav- 
ored to support the one we are reviewing upon 
scientific grounds ; he has fallen, however, into 
gross errors. And if he obtained the results he 
looked for from his observations, the reason was 
that he had taken his measures so that it was 
impossible it should have been otherwise, since 
he extended his observations over a greater or 
less number of days, accordingly as he had need 
of a greater or less number of atmospheric 
changes. 

Finally, it has been asked whether it is not 
possible that aerolites come from the moon, and 
the conjecture has been supported, among 
other grounds, by observations, which would 
seem to prove that this planet possesses nume- 
rous volcanoes. We must remark, in the first 
place, that the appearance on the surface of the 
moon at different intervals of time, of self-lumi- 
nous points, and the crater-like form affected by 
almost all the cavities observed, are not suffi- 
cient to establish the existence of volcanoes in 
the moon. For the rest, it is very true that, the 
existence of these volcanoes being admitted, 
stones might be shot from them with a force 
sufficient to carry them out of the sphere of the 
moon's attraction. It has been calculated that 
for this purpose, no greater velocity would be 
needed than five and a half times that of a can- 
non-ball ; and our volcanoes have sometimes 
thrown out rocks which must have issued from 
their craters with a greater velocity than that, 
to reach the distance at which they fell. We 
shall take a review of the different hypotheses 
by which this astonishing phenomenon has been 
sought to be explained. 

And first, we shall enumerate the general cir- 
cumstances observed with regard to meteoric 
stones, and which the hypotheses ought to suffice 
to explain in order to gain admission. 

Aerolites are usually accompanied by an igneous 
meteor of the kind named bolides, or fire balls. 
They are all composed of the same chemical 
constituents, almost in the same proportions. We 
find in them a considerable quantity of silex, 
and of iron, sulphur, nickel, manganese, and 
chromium. There fell some at Alaix in Lan- 
guedoc, which contained also a small quantity 
of carbon ; but perhaps those which fell else- 
where had also contained some, which they 
had lost in passing through the atmosphere : for 
these stones endure such a degree of heat in 
passing through the air as must dissipate a con 
siderable part of whatever volatile or combusti- 
ble principles they may originally have possess- 
ed. It is of importance to observe that the iron 
and nickel they contain is in the metallic sta*e, 
which is not the case in those aggregations of 
metals that are found on the surface of the 
earth. It is certain, moreover, that these stones 
themselves are not naturally to be found on any 
part of the surface of our globe. All those that 
are known have fallen from the air. 



34 



Arago and Lardner's Astronomy. 



Such are the facts; the suggestions offered 
for their explanation may be reduced to the 
three following hypotheses. 

1. It has been supposed that aerolites were, 
like ram and hail, true meteors formed by ag- 
gregation in the atmosphere. 

2. Chladni thought they were fragments of 
planets, or even small planets, which, circula- 
ting in space, entered the terrestrial atmosphere, 
and gradually losing their velocity, in conse- 
quence of the resistance of the air, fell at last on 
the surface of the earth. 

3. Lastly, the author of the Mecanique Celeste 
has remarked, that aerolites might possibly de- j 
rive their origin from some lunar volcano, which 
should fling them to a sufficient distance from j 
the moon to enable them to become new satel- 
lites to the earth, but satellites, which having so 
much the less mass, should be subject to so 
much the greater perturbations. If, after circu- ! 
lating for a longer or shorter period in space, 
the small body should at last be carried with- 
in the radius of the earth's atmosphere, its ve- 
locity would necessarily be destroyed, as in the 
last hypothesis, and it would finally fall to the 
ground. \ 

Of these three theories, the first, which at the 
first glance appears the simplest and the most 
natural, is nevertheless the most improbable : it 
will not even bear examination. 

For in fact, that aerolites should form by way 
of aggregation in the atmosphere, it would be 
necessary that their constituent elements should 
previously exist there, That water and hail are 
formed in the air, is owing to the fact that the 
latter is always charged with watery vapors, 
and that cold is enough to condense them : but 
the most exact analysis has never discovered in 
the air any of the constituent principles of me- 
teoric stones. We find in it neither sulphur, nor 
silex, nor nickel, nor manganese, nor iron : 
there is even no proof that oxygen and azote, 
the constituent principles of atmospheric air, 
can dissolve such substances. But here we are 
met with an objection. All these analyses, it 
is said, are made with air taken from the surface 
of the earth : now who knows, but in the higher 
regions, there may be gases capable of holding 
in solution the metals and the earths of which 
aerolites are formed? To this we reply, that 
air has been analyzed taken from the greatest 
elevations to which man has ascended, and that 
its composition has been found absolutely the 
same as that of the air on the surface ; a result 
moreover which might have been anticipated, 
since it is a general law of the statics of gases, 
that they expand in time over the whole space 
which is open to them, and that when we lay 
one over another, several of different natures or 
specific gravities, they mingle at last together, 
so as to form a thoroughly homogeneous com- 
pound. If, therefore, there existed in the higher 
regions of the atmosphere gases capable of hold- 
ing in solution earthy or metallic matters, we 
should necessarily see something of this on the 
surface of the earth ; and since that is not the 
ca6e, the objection we are combating must con- 
sequently be unfounded. 

To the first impossibility are added several 
others. Though it were admitted that the con- 
stituent elements of aerolites really existed in 



the atmosphere, at all heights, and only escaped 
analysis because they are in such small quantity, 
it would still be necessary to explain with such 
feeble and such dispersed elements, a sudden 
precipitation, yielding stones of several quintals, 
such as those preserved at Ensenheim, in Alsace, 
or 3000 or 4000 stones of various dimensions, 
like those which were separated and shot off by 
the Laigle meteor. It would be necessary to 
assign the cause that combines the scattered 
molecules, and forms them into a single mass. It 
is not affinity, for the elements composing aero- 
lites are not in a state of combination, but simply 
agglomerated and held together in juxta posi- 
tion. And yet if they are not subjected to any 
force, these little globules ought to fall separate- 
ly as they are formed. It is in vain to object 
that they might be suspended for more or less 
time by a cause analogous to that, which, ac- 
cording to the ingenious opinion of Volta, balan- 
ces the particles of hail between two clouds, so 
as to give them time to enlarge by the addition 
of new layers of ice. The fact still remains, 
that these latter have never been seen to amount 
to several quintals, though the elements that 
form hail are much more abundant in the air 
than those of aerolites are supposed to be. Be- 
sides, in Volta's theory, the suspension of hail in 
the atmosphere is attributed to the reciprocal 
action of electric clouds, a cause which cannot 
be in like manner adapted to the formation of 
aerolites, since the meteors that carry them 
sometimes burst in the clearest weather. Lastly, 
if aerolites were formed in the air like rain or 
hail, they would like them obey the laws of 
gravitation, and would fall to the earth in a 
right line, or at least without any other devia- 
tion from it than that occasioned by the force of 
the winds. But this is not the case. Aerolites 
exhibit in their fall a very considerable horizon- 
tal velocity, sometimes comparable to that with 
which the earth moves in its orbit. This alone 
would be sufficient completely to exclude the 
possibility of their formation in the atmosphere, 
even had not the chemical reasons we have sta- 
ted already induced us to discountenance the 
idea. 

The second hypothesis respecting the origin 
of these masses is much more plausible. There 
have lately been discovered such very small 
planets, that we must not revolt against admit- 
ting it as possible that still smaller may exist, 
and such that our meteoric stones might proceed 
from them. These little planets entering the 
atmosphere of the earth, and there gradually 
losing their velocity, would at last fall upon its 
surface ; but that could not occur without a con- 
siderable compression of the air in front of the 
moving body, a pressure which might no doubt 
be sufficiently powerful to disengage such a 
quantity of caloric, that the stony mass might 
be heated to a high degree, and that its volatile 
elements might be inflamed. This hypothesis 
then accords perfectly with all the circumstan- 
ces of the fall of meteoric stones, but it does not 
in any manner account for their identity of com- 
position, or at least it can only explain it by sup- 
posing that all the planets small enough to form 
meteoric stones are absolutely of the same na- 
ture, and composed of the same elements, in the 
game proportions ; a supposition at variance with 



Arago and Lardner''s Astronomy. 



35 



observation, as regards the earth, and which ex- 
tended to the other celestial bodies, becomes, if 
we consider the generality of their nature, ex- 
cessively improbable. 

On the contrary, this identity of chemical 
composition accords surprisingly with the last 
theory, which supposes these stones to issue 
from a volcano in the moon : for in this case it is 
enough to suppose that the lunar volcanoes only 
project such substances, or that they are peculiar 
to a single one of them, which alone has the 
power of emitting them with sufficient force to 
make them satellites of the earth : and this de- 
gree of force, which has been ascertained by 
calculation, is, as we have seen, very inconsider- 
able, because the moon is not surrounded with 
a resisting atmosphere. Bur, as we stated in the 
outset, though the existence of volcanoes in the 
moon is rendered probable by astronomical ob- 
servations, it is not yet established. Otherwise, 
these volcanoes once admitted, the explana- 
tion of the phenomenon becomes a mere ques- 
tion of simple mechanics. We may imagine be- 
tween the earth and the moon a certain surface 
marking the limits of the space, within which 
each of these bodies possesses a paramount at- 
traction. This limit will be nearer to the moon 
than to the earth, because the former body is 
much the smaller. Once the stone discharged 
by the luuar volcano is arrived beyond this lim- 
it, a thing which may occur in an infinity of di- 
rections, it becomes a satellite of the earth, but 
a satellite which undergoes enormous perturba- 
tion on account of its small mass compared with 
those of the earth, the moon, and the sun, by 
which it is attracted. Should the effect of these 
perturbations once be to entangle it in the earth's 
atmosphere, the resistance of that atmosphere 
will soon exhaust its velocity, and it will fall to 
the earth as in the preceding case. 

Thus we are led to see that the theory de- 
riving aerolites from volcanoes in the moon, is 
the most probable of all, and hitherto the only 
one that satisfies all the phenomena observed ; 
hut we repeat, it is a simple hypothesis, and the 
existence of lunar volcanoes is in nowise demon- 
strated. 

* The physical condition of the moon is better 
known to us, than that of any other object in 
the universe beyond the limits of the earth. 
This is the necessary and natural consequence 
of its proximity. The nearest planets to the earth 
are Mars and Venus, the former when in oppo- 
sition, the latter when in inferior conjunction. 
But Venus in this position is not visible, her 
dark side being turned toward us. Mars, how- 
ever, in opposition, is seen under very advan- 
tageous circumstances. His distance, however, 
even then is about fifty millions of miles, while 
that of the moon is scarcely a quarter of a million 
of miles; thus the planet which approaches near- 
est to the earth, is still two hundred times more 
distant than the moon. Nevertheless, with all 
the improvement that telescopes have under- 
gone, our powers of direct observation of the 
moon are limited. A telescope, for example, 
which would magnify a thousand times, (a 
power which could scarcely be applied to such 
an inquiry) would enable us to see the moon as I 
we should see it with the naked eye at a distance I 
of two hundred and fifty miles. We could not, | 



therefore, even by such means discover any tra- 
ces upon it of a vegetable or animal creation, 
or artificial structures if any such existed. The 
question, therefore, whether the moon be an in- 
habited globe, can only be decided^on grounds of 
probability and analogy. It has no atmosphere, 
and, as a consequence of this, its temperature 
must be lower than that of the summits of the 
most lofty parts of the Alps or the Andes; these 
are enveloped in eternal snow, because the air 
at such elevations is too attenuated to collect or 
retain enough of the sun's heat to produce a 
temperature above the freezing point ; the tem- 
perature on the moon in the utter absence of an 
atmosphere, must be much lower. The atmo- 
sphere and clouds being the agents by which that 
diffusion of solar light is produced, which consti- 
tutes the common and general light of day, on 
the moon there cau be no light except there only 
where the sun shines. The atmosphere is the me- 
dium of sound ; there can therefore be no sound 
upon the moon. There can be no fluid matter, and 
therefore no conceivable organization. In a word 
all the analogies conspire to prove the position, 
that the moon is not an inhabited globe. 

* The observations of Cassini, Herschel, and. 
others made upon the moon, are curious and in- 
teresting. On the 4th of May 1783, Herschel 
observed a luminous spot on the dark part of 
the moon. On the 19th of April 1787, the same 
luminous point reappeared, still more bright: 
these and similar appearances have been ascrib- 
ed to active volcanoes upon the moon. 

* If the moon were inhabited, an observer 
upon it would be presented with some curious 
and interesting appearances in the firmament, 
The days would be about twenty-seven times 
longer than ours. The transition, at sunset and 
sunrise, from light to darkness, or vice versa, 
would be instantaneous and complete ; no at- 
mosphere being present to produce twilight. In 
high latitudes, the sun would never rise to any 
considerable altitude, and near the line, though 
the sun would be nearly vertical for a long time 
during the day, the night would be so protract- 
ed, that the most intense cold would be produ- 
ced by the long absence of the solar heat. The 
days and nights would be always equal, there 
being no inclination of the axis sufficient to pro- 
duce an appreciable difference of seasons. The 
inhabitants of one hemisphere would never see 
the earth, except by travelling into the other 
hemisphere. The inhabitants of the latter would 
see our globe as a moon in the firmament, thir- 
teen times larger than the moon appears to us. 
The geographical features of our globe would, 
be discoverable, and the polar snows would be 
visible to them as those of Mars are to us by the 
aid of the telescope. The diurnal rotation of 
the earth wotdd he distinctly visible, and it 
would present daily all the variety of phases 
which the moon exhibits to us monthly. Our 
globe would appear stationary in their firma- 
ment, always seen at the same point. The fir- 
mament would however appear to revolve, leav- 
ing, as it were, the earth behind it. .v selenite, 
dwelling at the centre of the visible hemisphere 
of the moon, would see the earth constantly 
suspended in iris zenith. Those who might 
dwell near the border of that hemisphere, would 
see the earth at a low altitude in their frnia- 



36 



Arago and Lardner's Astronomy 



merit, but always at the same altitude. By trav- I] other hemisphere. The earth would therefore 
elling toward the edge the earth would seem to j serve as an easy means of the observer ascer- 
set. and finally to disappear on passing into the li taining his own position on the moon. 



LECTURE VI 



THE PLANETS. 



Mercury $. 

Mercury is the nearest planet to the sun. 
It appears in the evening after sun-set, in the 
western region of the heavens, under the form 
of a small but very brilliant disk, at first diffi- 
cult to distinguish on account of the twilight, 
but becoming more and more brilliant in pro- 
portion as its distance from the sun increases, 
until arrived at a certain limit, it seems for a 
while to remain motionless. The first part of 
its course is direct, like that of the stars, but it 
is not long before it retraces its path and disap- 
pears entirely. Soon after this it reappears in 
the morning in the east, some time before the 
rising of the sun, withdraws from it more and 
more up to a point, where it again becomes sta- 
tionary, again to retrace its path, plunge into 
the sun's rays and reappear anew after its setting. 

The brief duration of its appearance arises j 
from its closeness to the sun, from which it ap- 
pears to be separated but from sixteen to twen- 
ty-nine degrees : its direct distance from the 
sun is 37,143,000 miles: its apparent diameter 
is about seven minutes, and its real diameter is 
aearly two-fifths that of the earth. It turns on 
its axis in 24h 5' 3", and accomplishes its orbit 
in 8?d23b 25' 44", with a velocity of 111,000 
miles an hour. This orbit, which is always com- 
prised within that of the earth, forms a very ec- 
centric ellipse, very much inclined to the plane 
of the planet's equator, and making with the 
plane of the ecliptic an angle of about seven de- 
grees. 

When Mercury in his retrogade movement 
plunges into the sun's rays, it sometimes hap- 
pens that he is seen traversing the sun's disk un- 
der the form of a black spot. It is he no doubt, 
for the position, the motion, and the diameter 
are the same. This is what is called the transit 
of Mercury : it does not take place for us in every 
revolution, on account of the inclination of its 
orbit to the plane of the ecliptic : we can only 
tee the planet on the sun's disk, when the for- 
mer is in the point of its orbit's intersection with 
the ecliptic, and when the line connecting its 
centre with that of the sun, passes also through 
the centre of the earth. The smallness of this 
planet however, its distance from the earth, and 
its proximity to the sun, frequently prevent us 
from witnessing its transits, which regularly re- 
cur after periods of six, seven, thirteen, forty-six, 
and 263 years. 

PHYSICAL CONSTITUTION OF MERCURY. 

Mercury is of a perfectly spherical form. Like 
all the planets, it borrows its light from the sun : 
this is proved both by its transits across the sun's 



disk, during which it appears as a dark spot, 
and by the phases it presents, which may be 
observed with the help of a telescope like those 
of the moon. 

By means of this instrument, it has also been 
discovered that one horn of its crescent is trun- 
cated ; and it is this truncature that has enabled 
us to determine the period of its rotation, for this 
planet has no spots on its surface : it is an effect 
of the asperities that no doubt ruffle its surface, 
and which in a certain position screen from our 
view some of the points illuminated by the sun. 

It is thought that Mercury is enveloped by an 
extremely dense atmosphere. Its motion from 
point to point in space, is more rapid than that of 
the other planets, because it is nearer the sun. 
The latter appears to it thrice as great as to us, 
and Newton has calculated that it transmits to it 
a heat seven times that of our torrid zone. But ' 
we must not conclude too hastily from thence, 
that the planet really sustains so highly exalted 
a temperature : we are not yet sufficiently ac- 
quainted with the causes that produce heat, to 
be at liberty tc establish this inference : on the 
contrary, it is very possible that the sun's rays 
may be modified in their action by the nature of 
the constituent elements of the different planets. 

Venus $. 

Venus is the most beautiful of all the stars ; it 
is for this reason she has received the name she 
bears. Like Mercury, she appears sometimes 
in the morning, sometimes in the evening, and 
6he is called the morning or the evening star, 
accordingly as she is seen before the rising, or 
after the setting of the sun. Some days after 
her conjunction with the sun she is seen first in 
the morning on the east of that luminary, under 
the form of a handsome crescent, the concavity 
of which is turned from the sun. She moves 
westward ; and as she proceeds, her motion be- 
comes slower, and her crescent enlarges, until 
at last she arrives at the point where she remains 
stationaiy for a time, being then in the form of a 
semicircle. She then sets off again toward the 
east, and gradually accelerates her motion till she 
arrives at the sun. Some time after this she is 
seen in the evening east of him, quite round, but 
very small ; she continues her course eastward, 
augmenting in diameter, but diminishing in 
roundness, till she again becomes a semicircle. 
Lastly, she again takes a western direction, con- 
stantly increasing in diameter, and presenting a 
crescent, and returns finally to conjunction with 
the sun. 

Venus's distance from the earth, like that of 
Mercury, is very variable, as is shown by the 
apparent variations in their diameters. Her 



Arago and Lardner's Astronomy. 



37 



mean distance from the sun is seventy millions 
of miles : her apparent diameter varies from 30" 
to 1S4". Her rotation on her axis takes place 
in 23 h 21' 19", and the period of her revolution 
round the sun is 224 d 16 h 49'. Her orbit is in- 
clined 2° 24' to the ecliptic, and is always in- 
closed within that of the earth. 

Venus, as well as Mercury, exhibits transits 
over the sun's disk, and like' him appears then 
under the form of a dark spot. These phenom- 
ena are very rare, and astronomers avail them- 
selves of them to measure her distance with ac- 
curacy. We have elsewhere mentioned, that by 
means of these transitions the sun's parallax has 
been obtained to within a tenth of a second. 

APPEARANCES OF VENUS AS SHE MOVES ROUND 
THE SUN. * 

Fig. 25. 



^ 



? 
u 



r 



PHYSICAL CONSTITUTION OF VENUS. 

When this planet is projected on the disk of 
the sun, she takes the form of a small round 
black spot: her figure is therefore spherical, 
and her light borrowed from the sun, as we al- 
ready had reason to conclude from observing her 
phases. 

The duration of her rotary motion has been 
determined, as in the case of Mercury, by ob- 
serving the asperities of her surface, which, in- 
tercepting the light she reflects, give a truncated 
form to the horns of her crescent ; the length of 
her day is the same as the interval elapsing be- 
tween two successive appearances of the ob- 
served truncature. This planet is enveloped in 
an atmosphere : a German astronomer arrived 
at this conclusion by calculations founded on the 
laws of the degradation of light, and the fact is 
established, that her illuminated portion is larger 
than it should be, were it not for refraction. 

Although almost as large as the earth, Venus 
moves with more rapidity, because she is nearer 
the sun. This luminary appears to her twice as 
large as it does to the earth, and Mercury is her 
morning and evening star, as she is ours. 

The axis of Venus is inclined 75 degrees to 
her orbit ; that is, 51 and a half degrees more 
than the earth's axis to the ecliptic. The north- 
ern pole of her axis points toward the 20th de- 
gree of Aquarius, in a direction from Cancer ; 
consequently the northern regions of Venus have 
summer in those signs in which we have winter, 
and vice versa. As the greatest inclination of 
the sun on each side of her equator amounts to 
75 degrees, her tropics are 15 degrees from her 
poles, and her polar circles at the same distance 
from her equator. She has, therefore, at her 
equator, two summers and two winters, in each 
of her annual revolutions. 

Numerous endeavors have been made to as- 
certain whether Mercury and Venus have satel- 
lites, but none have been discovered, and it is 
highly probable that these have only been given 
to the superior planets. 

* The inferior planets were both known to 
the ancients, although Mercury can be rarely 
discovered by the naked eye. It is said that 
Copernicus himself never saw this planet. One 
of the opponents of the system of Copernicus 
urged, as an invincible argument against that 
system, that, if it were true, the planets Mercu- 
ry and "Venus ought to present to us all the va- 
rious phases of the moon. Such anidea seemed 
at the time so chimerical, that it required all the 
sagacity and moral courage of Copernicus to 
imagine the answer, and to venture to utter it. 
That illustrious discoverer saw instinctively, the 
truth of the consequence alleged as an insuper- 
able objection, and instantly replied, that " such 
indeed must be the case, and if we could see 
Venus as plainly as we see the moon, we should 
find that she would exhibit the same change of 
appearance." The invention of the telescope 
soon after, enabled Galileo to see these very 
phases, and literally to realize the anticipation 
of Copernicus. 

* Cassini and Schroeter ascertained the diur- 
nal rotation of Venus, and observed that the axis 
on which this rotation takes place, is inclined at 
an angle of 15° with the plane of the ecliptic ; 



3S 



Arago and Lardner's Astronomy. 



and it seems probable that the inclination of the 
axis of Mercury is nearly the same. These 
points are, however, not so certainly known as 
the position of the axes of the superior planets. 
It is certain, however, that the time of rotation, 
both of Venus and Mercury, is nearly the same 
as that of the earth; and, consequently, the 
average length of the days and nights is the 
same. It is supposed that the mountains on Ve- 
nus are about four times as high as those on the 
earth. 

* To the inhabitants of Venus, Mercury ap- 
pears as a morning and evening star, as Venus 
does to us ; and the earth presents the same ap- 
parent motion in the heavens as Mars does to us, 
but appears fifteen or sixteen times brighter and 
larger. With telescopes, the geographical fea- 
tures of the earth would be easily seen by the 
inhabitants of Venus. 

* The sun appears to Mercury six times, and 
to Venus twice as large as to the earth, and con- 
sequently, transmits to them respectively more 
light in the same proportions. But the light and 
warmth received by us from the 6un, depends, 
in so important a manner on the agency of our 
atmosphere, that it is impossible, with our pres- 
ent knowledge, to say how the illuminating and 
heating power of the sun's rays may be modified 
by a similar agency on the different planets. It 
is easy to imagine simple and very slight modi- 
fications in the density of the air, the produc- 
tion of clouds, and the magnitude of the pupil of 
the eye, by which the inhabitants of all the 
planets would, in fact, enjoy the same degree of 
light and warmth. 

SUPERIOR PLANETS. 

The two planets of which we have just spoken 
are called inferior, because, as we have already 
said, they are less distant than the earth from 
the sun : those to which we are now about to 
direct our attention are called superior, in oppo 
sition to the others, because the earth is nearer 
than they to the sun. 

Mars J\ 

This planet comes immediately after our earth 
in respect of distance from the sun. It appears 
to move from west to east round the sun, but 
its motion exhibits numerous irregularities. In 
the morning, when it begins to separate from 
the sun, its course is very rapid ; but this rapid- 
ity diminishes gradually, and. ceases altogether 
at about 137 degrees. The planet then takes a 
direct motion, which brings it in opposition with 
the sun ; its rapidity then progressively dimin- 
ishes, and it seems to retrograde till it has passed 
the sun 137 degrees : its motion then becomes 
once more direct, till at last the planet plunges 
into the sun's rays. 

The mean distance of Mars from the sun is 
146 millions of miles. As its distance from the 
earth is very variable, this variation exhibits its 
effects in the apparent dimensions of its diame- 
ter, which is sometimes 18", sometimes 90''. Ob- 
servations of the spots on his disk show, that 
IVIars revolves on his axis in 24'» 31' 22". He 
moves in a very eccentric ellipse, which he 
travels over in 686d 23^ 30' 41". 4. His axis is 
inclined 61° 33', and the inclination of his orbit 
to the ecliptic is 1° 51' 1". His equatorial is to 



his polar diameter in the proportion of 16 to 
15. 

Mars undergoes great variations of distance in 
his course through his orbit ; sometimes he ap- 
pears near, sometimes far from the sun ; some- 
times he rises when that luminary sets, and sets 
when he rises : his distance, too, from the earth 
varies prodigiouly, being less in opposition, 
greater in conjunction. He exhibits the phenom- 
ena of phases as well as Mercury and Venus, 
but unlike them, never appears as a crescent. 

PHYSICAL CONSTITUTION OF MARS. 

When this planet is observed through a tele- 
scope it exhibits a round disk, which, never ap- 
pearing indented, has probably few asperities. 
Its phases prove that it has no light of its own. 
On its surface are seen spots of various tints, by 
the aid of which the period of its rotation has 
been determined. The light reflected by Mars 
is a dark red, owing, it is presumed, to his at- 
mosphere, which is so deep and dense, that 
when he approaches any star, the latter changes 
color, grows dim, and often disappears, though 
it be at some distance from the body of the 
planet. 

Besides the spots, which have served for de- 
termining the period of Mars's rotation, several 
astronomers have remarked, that a segment of 
his globe toward his south pole has a lustre so 
superior to that of the remainder of his disk, 
that it seems like a segment of a larger globe. 
Maraldi informs us that this brilliant spot was 
observed sixty years ago, and that it was the 
most permanent of all. A part of this planet is 
more brilliant than the rest : the darker portion 
is subject to great changes, and at times disap- 
pears. A similar brilliancy has often been ob- 
served at the northern pole. These observations 
have been confirmed by Herschel, who exam- 
ined the planet with more powerful and better 
constructed instruments than had been employed 
before his time. According to this astronomer, 
the analogy between Mars and Venus is the 
greatest presented throughout the solar system. 
Both bodies have almost the same diurnal mo- 
tion : the obliquities of their orbits present 
but little difference. Of all the superior planets, 
Mai s is that whose distance from the sun differs 
the least from the earth's, and the length of his 
year does not much differ from ours, in compari- 
son with the extreme duration of those of Jupi- 
rer, Saturn, and Herschel. Since the globe we 
inhabit has its icy polar regions, and mountains 
covered with snow and ice, which melt but par- 
tially when they are alternately exposed to the 
action of the sun, it is reasonable to suppose that 
the same causes produce the same effects upon 
Mars, and that these lustrous polar spots are 
owing to the vivid reflection of light from those 
icy regions ; and that the diminution of these 
spots, when they are exposed to the sun's rays, 
is caused by the influence of that luminary. 
The south polar spot was extremely brilliant in 
1781, which might have been expected, since 
that pole was then issuing from a night of twelve 
months' duration, during all which time it had 
been deprived of the light of the sun: it was 
smaller in 1783, and diminished gradually, from 
the 20th of May to the middle of September, 
when it seemed to grow stationary. At this 



Arago and Lardner's Astronomy. 



39 



epoch the southern pole had enjoyed eight 
moths' summer, during which it had constantly- 
undergone the influence of the sun's rays. It is 
true that, toward the close of this period, they 
were so oblique that they could not act very 
strongly upon the region in question. On the 
other hand the northern pole, which, from an 
exposure of twelve months to the sun, had fal- 
len into deep obscurity, appeared of small di- 
mensions, though it had, no doubt, increased in 
volume. It was not visible in 1783, on account 
of the position of the axis, which did not allow 
us to see this pole. 

Another consideration adds strength to the hy- 
pothesis, that the brilliant spots about the poles 
of iMars are caused by the presence of snow and 
ice, namely, that the axis of this planet being 
inclined at an angle of 60° 35' to its orbit, the 
variations of the seasons cannot be very extreme, 
and this constancy of each parallel in preserving 
the same temperature, is regarded as favorable 
to the formation of ice. 

The sun affords to Mars only a third of the 
quantity of light, or thereabouts, which he sheds 
on the earth ;* it appears strange, therefore, that 
this planet has no moon or satellite. This cir- 
cumstance, however, may be compensated for 
by the depth and density of its atmosphere, 
which we have seen to be considerable. 

* The four planets, Mercury, Venus, the Earth 
and Mars, present so many points of resemblance 
and mutual analogies, and differ in so many re- 
spects from the other planets, that they are some- 
times regarded as a distinct class, and called the 
Terrestrial Planets. They have the same order 
of magnitude, the same days and nights, are sim- 
ilar in their geographical character, are diversified 
by climates and zones, are supplied with atmo- 
spheres and clouds, and are theatres for the same 
play of meteorological phenomena. These form 
a body of circumstantial evidence which justify 
the conclusion that they are inhabited globes, in 
all respects similar to the earth. Of late years, 
Beer and Maraldi, two eminent Prussian astron- 
omers, have carried on a course of systematic 
and well conducted telescopic observations, with 
a view of determining the physical constitution 
of the globe of Mars ; and their labors have af- 
forded us a very exact delineation of the promi- 
nent marks upon it, as distinguished from those 
shifting and variable features which proceed 
from atmospheric causes. The permanent marks 
must be geographical, and analogy justifies the 
conclusion arrived at by Sir John Herschel, that 
they are land and water. The position of the 
axis of Mars is well known, and agrees almost 
exactly with that of the earth. Not only, then, 
is there on Mars the same succession of seasons, 
but the extremes of these seasons are circum- 
scribed within the same limits, and, for the same 
reason, the same observation will be applicable 
to the climates which diversify its surface. 

THE FOUR TELESCOPIC PLANETS. 

These planets, which are situated in the solar 
system, between Mars and Jupiter, are discove- 
ries of modern date. To this circumstance, com- 

*The respective quantities are more accurately as 12 
and 27, these numbers representing nearly the inverse 
proportion of the squares of the distances from the Sun, 
of the earth and Mars. 



bined with their small size and distances, it is 
owing that they are very little known. 

Juno ^. 

This planet, discovered by Harding, the 1st of 
September, 1803, is 1320 miles in diameter, ac- 
cording to Schroeter. It takes 4 years 128 days 
to complete its revolution round the sun, in an 
orbit inclined 23° 4^' to the ecliptic : its dis- 
tance from the sun is about 256 millions of miles. 

Ceres ?• 
Of the four telescopic planets, Ceres was the 
first discovered, by Piazzi, the 1st of January, 
1801 . Its diameter, 140 miles according to Hers- 
chel, 1320 according to Schroeter, is not well 
known. It makes its revolution round the sun 
in four years and a half, in an orbit inclined 10° 
37' 25" to the plane of the ecliptic. Its distance 
from the sun is about 264 millions of miles. Its 
appearance is that of a nebulous star, surrounded 
by very vai-iable mists, which induced Herschel 
to suppose it possessed of an atmosphere. 

Pallas $ . 

This planet was discovered by Olbers, the 28th 
of March, 1802. Schroeter assigns it a diame- 
ter of 1950 miles, and Herschel one of but 140. 
Its extremely elongated orbit is the most oblique 
of all to the ecliptic, making with it an angle of 
34° 37' 30". This orbit it describes in four 
years, seven months, and eleven days. Its dis- 
tance from the sun is 267 millions of miles ; its 
color is whitish, and it appears rather indistinct, 
even with a powerful instrument. 

Vesta g. 

Vesta was discovered by a pupil of Olbers, 
the 29th of March, 1807. It describes its orbit 
in three years, sixty-six days, four hours ; this 
appears very irregular, and is inclined 7° 8' to 
the ecliptic. This small planet is very little 
known. When observed by Herschel, with an 
instrument of great magnifying power, it did not 
present the appearance of a disk, but only ap- 
peared as a brilliant point. It is thought to be 
225 millions of miles from the sun. 

Though the dimensions of these four planets 
be not yet thoroughly known, we may, however, 
assert that they are extremely small, compared 
with those in their vicinity, and with regard to 
their distance from the sun. Another anomaly 
they present is, that they deviate considerably 
from the zodiac or the path of the planets. These 
considerations have given rise to a bold conjec- 
ture, namely, that these four little planets may, 
possibly, be but the fragments of a single planet 
formerly situated between Mars and Jupiter. 
This opinion acquires a high degree of probabili- 
ty, if to the preceding grounds we add that these 
planets are not round, as is indicated by the in- 
stantaneous diminution of their light when they 
present their angular faces, and that the intersec- 
tion of their orbits, whereby they all successively 
pass through the same point, is strictly in accord- 
ance with what would be required by the laws 
of mechanics in the case in question. In fact, 
according to these laws, were a planet to burst 
violently, each of its fragments, after describing 
a new orbit, would return and pass through the 
point where the explosion had taken place. 



40 



Arago mid Lardner's Astronomy. 



* The magnitudes of the asteroids are extreme- 
ly uncertain, but all astronomers agree that they 
are incomparably smaller than any of the other 
planets, or even of the satellites. Herschel, 
Schroeter, and other astronomers, have estimat- 
ed that the volume of the planet Vesta cannot 
be more than the twenty-five thousandth part of 
that of the earth. Herschel thinks that the di- 
ameter of Ceres does not amount to two hun- 
dred miles, and it seems that the bulk of Juno 
is somewhat greater than that of Vesta. Pallas 
is considered to be the greatest of the four, yet, 
according to Schroeter, it is less in magnitude 
than our moon. It has been calculated that the 
bulk of all the four together does not amount to 
the twenty-fifth part of our globe. If such bodies 
were inhabited like the earth, how easily would 
the inhabitants become acquainted with their en- 
tire surfaces. Taking the common estimate of 
the magnitude of Vesta, ten days would be suffi- 
cient for an active pedestrian to visit his anti- 
nodes, and a horseman in the same time might 



make a tour of the entire globe. The surface 
of such a globe would not exceed the magnitude 
of some of the smaller States of this Union. 
The smallness of these planets have rendered 
impracticable the discovery of their diurnal mo 
tion. Vesta, the brightest of the four, though 
the smallest in magnitude, appears like a star of 
the fifth or sixth magnitude. Schroeter, for this 
reason, conjectured that it might be a self-shi- 
ning body. The three others appear like stars of 
the ninth and tenth magnitudes. Ceres is char 
acterized by a very varying light; sometimes 
bright and reddish — sometimespale and whitish; 
an effect probably owing to its irregular shape. 
These planets present singular atmospheric ap- 
pearances. Ceres and Pallas especially, are in- 
closed iu atmospheres from twelve to fifteen times 
the height of ours. The inclination of their or- 
bits, especially those of Juno and Pallas, is con- 
siderable, causing these planets to move beyond 
the limits of the zodiac, whence they are some- 
times called ultra zodiacal planets. 



LECTUEE VII. 

THE PL AN ETS.— (Continued.) 



Jupiter %, and his satellites. 

Jupiter is the largest of the planets, and, 
next to Venus, the most brilliant. It is 1470 
times the size of the earth, and it is owing to 
its prodigious distance from us, that it appears 
so small. Its movement on its axis is extremely 
rapid, being completed in 9b 56'. Its revolution 
round the sun takes place in 4332*596^, in an 
ellipse, making an angle of 86° 47' 36" with the 
ecliptic. The distance at which Jupiter is 
placed, does not allow of our seeing the phases 
he no doubt undergoes, like all the other 
planets.* 

Seen through the telescope, Jupiter appears 
accompanied by four small luminous bodies, 
which revolve round him and are called his 
satellites. They are distinguished by their po- 
sition, the first being that nearest the planet. 
They move in orbits almost in the plane of his 
equator; the first in Id 13 h 27' 35"; the second 
in 3d 13h 13' 42"; the third in 7 d 3*» 42' 33"; the 
fourth in 16* 16 h 32' 8". 

The first three move in planes diverging but 
very little from each other, but the fourth in one 
rather more so: their orbits are almost circular; 
no eccentricity has been detected, except in 
those of the third and fourth ; that of the latter 
is more particularly discernible. 

The motions of the first three exhibit singular 
relations to each other. The mean sidereal mo- 
tion of the first, added to twice that of the third, 
is constantly equal to three times the mean mo- 
tion of the second; and the sidereal, or mean 
synodical longitude of the first, minus three 
« 

* The relative positions of Jupiter, the Earth and the 
Sun, reader the existence of phases to any observable 
extent impossible. 



times that of the second, plus twice that of the 
third, is always equal to two right angles. 

Herschel, on attentively examining these 
satellites through the telescope, perceived that 
the intensity of their light exhibited periodical 
variations, and by calculating the periods when 
their faces are turned toward us, he was able to 
determine the duration of the rotation round 
their axes. He found that they always turned 
the same face toward Jupiter, and thus made 
but one complete turn on their axes during the 
time of their describing an entire circumference 
of their orbits, thus strikingly confirming their 
analogy with the moon. Maraldi had already 
established this fact with regard to the fourth 
satellite, by observing the returns of one spot 
observed on its disk. 

When the satellites of Jupiter, in their revo- 
lution round him, happen to pass between him 
and the sun, they project, on the enlightened 
portion of his disk, a shadow varying with the 
distance and size of each of them. This then is 
a partial eclipse of the planet, and from it we 
infer that neither Jupiter nor his satellites are 
self-lustrous. 

When, on the other hand, the satellites pass 
behind the planet, they are seen successively to 
disappear; this is the eclipse of the satellites. 
The first three are eclipsed at every revolution, 
but the fourth has an orbit so oblique, that when 
in opposition to Jupiter, he escapes falling into 
the shadow two years in every six. We per- 
ceive, from the strange proportions we have 
mentioned, that, for a great number of years, at 
least, the first three satellites cannot be eclipsed 
together; for, in the simultaneous eclipses of the 
second and third, the first is constantly in con- 
junction with Jupiter, and vice versa. 



Arago and Lardner's Astronomy. 



41 



It has been remarked that 
these eclipses never take place 
from east to west, but on their 
return from west to east ; 
hence it follows that the sat- 
ellites revolve, like all the 
other planets of our system, 
from west to east. 

These eclipses of Jupiter's 
satellites have furnished the 
means, as we shall seeby-and- 
by, of determining the velo- 
city of light. We shall also 
see that they are of great use 
to navigators for determining 
the longitude. 

PHYSICAL CONSTITUTION OF 
JUPITER. 

We have seen that Jupiter, 
as well as his satellites, bor- 
rows his light from the sun. 
Though 1470 timeslarger than 
the earth, his density is but 
one-fourth of that of our pla- 
net. His form is that of a 
spheroid flattened at the poles: 
this flattening, which amounts 
to y 1 ^, is the effect of the rap- 
idity of bis rotary motion, as 
we shall show in speaking of 
theearth. His axis being near- 
ly perpendicular to the plane 
of his orbit, the sun is almost always in the plane 
of his equator, so that the variation of his sea- 
sons is almost insensible, and his days and nights 
are always nearly equal. 

The sun appears to Jupiter five times smaller 
than to us, and sends him twenty -five times less 
heat and light; but his nights are very short, 
and illuminated by four brilliant moons, one, at 
least, of which is always shining. 

When Jupiter is observed with a good tele- 
scope, a number of zones or bands are perceived 
browner than the rest of his disk : they are gen- 
erally paralled to the equator, but in other re- 
spects they are subject to great variations. 
Sometimes but one of them is seen, at others as 
many as eight. Sometimes they are not parallel 
to each other, and of variable dimensions; one 
of them often contracts, while that nearest to it 
dilates; they seem as it were to melt into each 
other. The time of their duration varies: some 
have been seen to keep the same form for 
three months, and new ones have been seen to 
form in an hour or two. The continuity of 
these bands is sometimes 
interrupted, which gives 
them a lacerated appear- 
ance. The spots and bands, 
which were observed the 
7th of April, 1792, are rep- 
resented in the annexed 
figure. They are consid- 
ered as the body of the 
planet, and the luminous 
parts as clouds carried 
along by the winds in dif- 
ferent directions and with 
different velocities. Other varieties of its appear- 
ance are given in the following diagrams. 



Fie:. 27. 




Fig. 28. 




Fig. 26. 




* Passing beyond the region occupied by the 
asteroids, we encounter a new order of planets. 
The same grounds which have suggested the 
grouping of the four terrestrial planets, lead to- 
a similar classification of the three remote plan- 
ets, Jupiter, Saturn, and Herschel. These are 
of another order of magnitude, Jupiter being 
thirteen hundred times, Saturn a thousand 
times, and Herschel nearly a hundred times 
larger than our globe. Jupiter is the most stu- 
pendous object in the system, and seen from the 
earth, it presents the appearance of a star of the 
first magnitude, and sometimes its splendor sur- 
passes even that of Venus. The discovery of 
Jupiter's moons, which was the first fruit of the 
invention of the telescope, forms a memorable 
epoch in astronomical history; the first and 
fourth of these bodies are nearly as large as 
Mercury, and the second and third about the 
size of our moon. The first makes its complete 
revolution round Jupiter, presenting all its va- 
rious phases every forty-four hours ; the second 
completes the same changes in three days and a 
half; the third in about a week, and the fourth 
in sixteen or seventeen days. These bodies 
have been called in the order of their distance 
from Jupiter, Hebe, Ganymede, Themis, and 
Metis — these names are, however, little used at 
present, and they are distinguished by the or- 
der of their distance from Jupiter, the first being 
the nearest. 

* They form with Jupiter a miniature system, 
in all respects similar to the solar system : the 
celebrated laws discovered by Kepler being all 
observed in it. An intei-esting analogy with 
our moon, seems probable from the observations 
of Herschel, inasmuch as there is reason to be- 
lieve that they all present the same hemisphere 



42 



Ar ago and Lardner's Astronomy. 



toward Jupiter. It is remarkable, also, that 
their motions round Jupiter are so regulated, 
that one of them at least, must be always full or 
nearly so. 

* The disk of Jupiter, seen from one of his 
satellites, must offer a singular and imposing 
spectacle. An observer placed upon the first 
satellite, would scarcely perceive Mars, the 
Earth, or the inferior planets; the disk of the 
6un would appear six, or seven-and-twenty 
times less than to us, while the enormous globe 
of Jupiter, suspended immediately in the firma- 
ment,^ would present a disk fifteen hundred 
times greater than that of our full moon. Such 
a disk would consequently cover a large portion 
of the heavens. 

Saturn T^, his ring and his satellites. 

Seen by the naked eye, Saturn presents the 
appearance of a nebulous star of a dull leaden 
lustre, and as its motion is very slow, it is hardly 
distinguished from a fixed star. It exhibils 
parallel to its equator a series of bands, like 
those of Jupiter, but fainter, and it was by 
means of them that Herschel determined the 
period of the planet's rotation; this it accom- 
plishes in ten hours and a half. The flattening 
of its poles is one-eleventh: it moves at the dis- 
tance of 915 millions of miles from the sun, in 
an orbit it describes in twenty-nine years, five 
months, fourteen days, and the inclination of 
which to the ecliptic is 2° 30'. This planet is 
900 times larger than the earth, and the sun 
sends to it but the ninetieth part of the light he 
dispenses to us. 

Like Jupiter, Saturn too has his satellites, 
seven in number; six move almost in the plane 
of the equator, but the seventh diverges sensibly 
from it, the inclination of its orbit being about 
thirty degrees. It is ascertained that it makes 
but one turn round its axis during the period of 
its revolution; and thuugh it has not yet been 
proved whether or not this is the ca9e with the 
others, analogy disposes us to believe it, for this 
equality in locomotion and rotation appears to 
be the law of secondary planets. 

The periods of revolution of the satellites of 
Saturn present somewhat considerable differ- 
ences. 

The first completes its mean sidereal revolu- 
tion in the space of 22^ 37' 23"; the second l d 8 h 
53' 9"; the third in l d 21 h 17' 26"; the fourth in 
2d 17 h 44' 51"; the fifth in 4 d 12 h 25' 11"; the 
sixth in 15 d 22 h 41' 14"; the seventh in 79 d 7 h 
54' 37". _ 

Saturn's satellites undergo frequent eclipses, 
Which serve like those of Jupiter to determine 
longitude, but their great distance renders the 
observation of them more difficult. 

Saturn, already so remarkable for the number 
of his satellites, is still more so for the ring with 
which he is enveloped. It is a luminous baud 
situated in the plane of the planet's equator, 
forming a kind of belt to it, but separated from 
it by a distance equal to its breadth. It appears 
under the form of an ellipse more or less elon- 
gated, according to the obliquity under which it 
is seen, arising from the various inclinations with 
respect to our position assumed by Saturn in his 
revolution round the sun. While the ring af- 
fects the elliptic form, the extremities of its ma- 



Fig. 29. 




jor axis are called anses, and in this condition, 
when the obliquity is not too great, stars may 
be seen between it and the planet. But when 
its position is such that the prolongation of its 
plane passes through the centre of the earth, it 
only shows us its edge, and the angle it then 
subtends is so small, that it needs a very power- 
fully magnifying instrument to make it visible. 
It appears then as a luminous thread, dividing 
the planet's disk. 

When we use powerful telescopes, we dis- 
cover on the surface of the ring, several black 
lines, which seem to constitute so many separa- 
tions, but above all two rings are conspicuous, 
and of these Herschel has calculated the divis- 
ions. According to this astronomer, the interior 
diameter of the smaller ring is 146,345 miles, 
and the exterior diameter of the larger 204,883 ; 
the space between the two rings 2680 miles. 
Hence it would appear, that between the body 
of Saturn and the interior diameter of the inner 
ring, there is a distance of 70,000 miles. 

By means of the spots on the ring, Herschel 
has determined the duration of its rotation on its 
axis: it is I0 h 19' 16''. This axis of rotation is 
perpendicular to its plane, and is the same as 
that of Saturn. 

The duration of this rotation, which appears 
to be precisely that of a satellite having for its 
orbit the mean circumference of the ring, has 
enabled M. Biot to explain how the ring can 
sustain itself round the planet without touching 
it, or at least to connect this fact with the gene- 
ral cause that thus sustains all the satellites. 

In fact, he says, we may consider each part 
of the ring as a small satellite of Saturn, and the 
ring itself as an assemblage of satellites connect- 
ed together in an invariable manner. If these 
bodies were free and independent of each other, 
their velocity would vary with their distance 
from the centre of the planet; the nearest to the 
centre would move more rapidly, those farther 
off more slowly ; and if we take for a mean ve- 
locity that which answers to the mean circum- 
ference of the ring, the velocities of the other 
particles would differ from it, in excess or in de- 
ficiency, by an equal quantity. Now if the par- 
ticles become united and attached together so 
as to form a solid body, a sort of compensation 
will take place between their motions; the more 
rapid will communicate a part of their speed to 
the slower, and these again a part of their slow- 
ness to the former, and these opposite efforts 
mutually balancing each other, there will re- 
main only the mean velocity common to all the 
particles, which will be that of the mean cir- 
cumference. These rings will sustain them- 
selves round Safurn as the moon does round the 



Arago and Lardner's Astronomy. 



43 



earth, or as the arches of a bridge would do, if 
♦he centre of gravity were in the centre of the 
voussoirs. 

This theory would subsist, even though the 
ring should be composed, as appears to be the 
case, of several concentric rings detached from 
each other; only it would then be necessary to 
apply it separately to each of them, for the dura- 
tion of their several rotations would necessarily 
be different. 

Sometimes Saturn's ring, projecting itself on 
the disk of the planet, hides a part of it; and 
sometimes again, the planet conceals with its 
shadow a part of the ring. It follows from this 
that the ring is opaque like the planet, and that 
the light of both is borrowed. 

* When Galileo directed the first telescope to 
the examination of Saturn, he remarked that the 
planet appeared not as a single star, but like 
three together, nearly touching one another. 
He described them as having no relative motion, 
and as having the form of three o's thus, 0O0, 
the middle one being larger than those on each 
side of it. Such was the appearance which the 
ring presented to the imperfect telescope which 
he then possessed. At a later period, when the 
planet had changed its position, and probably 
had turned its edge to the sun, or to the earth, 
the ring disappeared, and the planet appeared a 
single round disk. Galileo expressed his aston- 
ishment. "Looking on Saturn," said he in a let- 
ter to Velser, " within these few days, I found it 
solitary, without the attendance of its accus- 
tomed stars, and in short, perfectly round and 
defiued, like Jupiter, and such it still remains. 
Now, what can be said of so strange a metamor- 
phosis? Are the two smaller stars consumed 
like the spots on the sun ? Have they suddenly 
vanished and fled? Or has Saturn devoured 
his own children? Or was the appearance in- 
deed fraud and delusion, with which the glasses 
have, for long a time, mocked me and so many 
others, who have observed with me ? " Although 
Galileo struggled hard to resolve this mystery, 
the discovery of the ring of Saturn, and its ob- 
liquity to the plane of the ecliptic, which alone 
could explain it, was reserved for future astrono- 
mers. The ring presents different appearances, 
according to the position of its plane with re- 
spect to the sun and the earth. When the di- 
rection of that plane passes between the sun and 
earth, the dark side of the ring is presented to 
us, and it is, therefore, invisible. When the 
edge of the ring is presented to the sun, the 
edge alone is illuminated, and being too thin to 
be seen at the distance of Saturn, the ring is in- 
visible on that account. When the edge of the 
ring is presented to the earth, it is the only part 
within view, and being too minute, is again in- 
visible. In short, the only circumstances in 
which the ring can be visible is, when its plane 
has such a position, that the same side of it is at 
once presented from the sun to the earth. 

* If the axis of Saturn move like that of Jupi- 
ter, perpendicular to its orbit, or nearly so, no 
part of the ring would ever be enlightened by 
the sun, except its edge. But the axis of Saturn 
being inclined to its orbit, at an angle of about 
60 degrees, and the plane of the ring, moving 
parallel to itself, and at right angles to that axis, 
it follows that the sun must illuminate one side 



of the ring, during one half of Saturn's periodical 
revolutions, and the other side during the other 
half. Recent observations made in Italy on the 
rings of Saturn, have led to the conjecture, that 
there are more than two of them. Besides the 
separation between the two rings discovered by 
Sir Wm. Herschel, three other dark streaks have 
been distinctly seen by observers at Rome, 
which would indicate five independent rings. 
This, however, cannot be considered as conclu- 
sively proved, until it has been submitted to 
some test, as unequivocal as that by which Sir 
Wm. Herschel proved the reality of the opening 
between the two rings discovered by him when 
he saw stars through it. It is not impossible 
that the dark concentric streaks observed on the 
surface of the ring, may proceed from some 
cause similar to that which produces the belts of 
this planet and Jupiter. These planets are in- 
vested with dense atmospheres, thickly loaded 
with clouds. They are of great magnitude, and 
revolve with extraordinary velocity on their 
axes. There are then present all the causes 
necessary to produce a series of atmospheric 
currents parallel to their equators, similar tc 
those which exist in our atmosphere, and are 
produced by the rotation of the earth ; but more 
energetic and permanent, in proportion to the 
greater velocity of rotation in the former bodies. 
These belts, then, must be regarded as an ar- 
rangement of clouds produced by such currents, 
and as the rings revolve in nearly the same time 
as Saturn, if they have an atmosphere, it will be 
subject to the same effects. 

* The appearance of the rings and moons must 
present a singular spectacle to the inhabitants of 
the planet. Duringonehalf of Saturn's revolution, 
the northern side of the ring is illuminated by the 
sun, and during that period, therefore, the inhab- 
itants of the northern hemisphere, or a portion of 
it, see perpetually suspended in their firmament a 
double bow, splendidly illuminated by the sun, 
apparent both by day and night. During the 
other half of the planet's revolution, the inhabi- 
tants of the southern hemisphere enjoy a like 
spectacle. An observer on the equator of Saturn 
being immediately under the edge of the ring, 
can only see that portion of it which catches the 
sun's light, and which will appear to him as a thin 
line of moonlight, extending from the eastern to 
the western point, to a certain elevation in the 
heavens. If he travel toward the pole on that 
hemisphere, toward which the illuminated side 
of the ring is turned, the ring will gradually be- 
gin to develope itself to his view, becoming a 
bow of moonlight, on which the shadow of the 
planet will fall to a greater or less extent, ac- 
cording to the relative positions of the sun, the 
planet, and the rings. As he travels to higher 
latitudes, the ring will appear a moonlight bow 
at a. less and less elevation in the heavens, until 
he shall attain the latitude of about sixty de- 
grees, when the ring will sink below the horizon 
and disappear. Above that latitude the curva- 
ture of the planet will intercept altogether the 
view of the ring. 

Herschel, or Uranus, HJ, and its satellites. 

This planet is of all the most, remote from the 
sun. and its orbit embraces that of all the others. 
Situated at a distance of more than 18-10 millions 



44 



At ago and hardness Astronomy. 



of miles, it accomplishes its revolution in eighty- 
four years. The inclination of its orbit to the 
ecliptic is but 46' 26". Its time of diurnal rota- 
tion is not determined. 

Hardly visible to the naked eye, it presents 
under the telescope a bluish white color. Its 
disk is well defined. It derives from the sun 
only the three hundred and sixty-second part of 
the light that we receive. 

When it was discovered, it was at first taken 
for a comet; but its proximity to the ecliptic 
showed soon that it was a planet. It had pre- 
viously been regarded as a fixed star. 

Herschel, who recognized it for a planet, dis- 
covered also its six satellites, which circulate 
round it nearly in the same plane. 

The first accomplishes its sidereal revolution 
in the space of 5d 21h 25' 21"; the second in 8 d 
16* 57' 47"; the third in 10 d 23^ 3' 59": the 
fourth in 13d 10h 56' 30"; the fifth in 38 d l h 48'; 
the sixth in 107a 16h 39' 56". 

* It was once suspected by Sir Wm. Herschel 
that Herschel or Uranus was attended by a 
double system of rings, at right-angles to each 
other, but this has never been confirmed by ob- 
servation. 

The following table will present a synopsis of 
all the circumstances of the volume, mass, den- 
sity, distance, motion, and inclination of the 
planets. 

DISTANCE OF THE PLANETS FROM THE SUN. 

Leagues. 

Mercury 13,361,000 

Venus 24,966,000 

The Earth 34,515,000 

Mars 52,390,000 

Vesta 81,330,000 

Juno 91,278.000 

Ceres 95,332,000 

Pallas 95,892,008 

Jupiter 179,375,000 

Saturn 329,200,000 

Uranus 662,144,000 

DIAMETERS OF THE SUN AND OF THE PLANETS, 
THAT OF THE EARTH BEING 1. 

The Sun 109-93 

Mercury 039 

Venus 0-97 

The Earth 1-00 

The Moon 0*27 

Mars 0-52 

Vesta "} 

Juno f T , , 

Ceres f Unknown - 

Pallas ) 

Jupiter 11-56 

Saturn 9-61 

Uranus 4-26 

VOLUME OF THE SUN AND OF THE PLANETS, THAT 
OF THE EARTH BEING 1. 

The Sun 1,328,460 

Mercury 0-1 

Venus 0-9 

The Earth 1 

The Moon 002 

Mars 0*2 

Juno ...7777.. 1 " ":'.. ( Unkno wn - 



H 



Unknown. 



Unknown. 



Ceres 

Pallas 

Jupiter 1470-2 

Saturn 887-3 

Uranus 77*5 

MASSES OF THE SUN AND OF THE PLANETS, THAT 
OF THE EARTH BEIl>G 1. 

The Sun 337-086 

Mercury 0*1664 

Venus 0-9452 

The Earth 1 

The Moon 0-017 

Mars 0-1324 

Vesta ") 

Juno 

Ceres 

Pallas ) 

Jupiter 314-8926 

Saturn 120-0782 

Uranus . 17-2829 

DENSITIES OF THE SUN AND OF THE PLANETS, 
THAT OF THE EARTH BEING 1. 

The Sun 0-23634 

Mercury 2879646 

Venus. 1-05701 

The Earth 1 

The Moon 0715076 

Mars 0-930736 

Vesta 1 

Juno f TT , 

Ceres f Unkuown - 

Pallas 3 

Jupiter 0-24119 

Saturn 0-095684 

Uranus 0-020802 

THE NUMBER OF FEET IN A SECOND THAT A HEAVY 
BODY WOULD FALL THROUGH AT THE SURFACE 
OF THE SUN AND PLANETS. 

The Sun 429 

Mercury 12 

Venus 18 

The Earth 16 

The Moon 3 

Vesta ~) 

Juno 

Ceres 

Pallas 3 

Jupiter 42 

Saturn 15 

Uranus , 4-2 

TIME OF ROTATION ON THE AXIS OF THE SUN AND 
PLANETS. 

D H M S 

The Sun 25 12 

Mercury .- 10 4 

Venus.! 23 21 

The Earth 10 

TheMoon 27 7 44 

Mars 1 39 22 

Vesta ~) 

Juno 

Ceres..-. 

Pallas 3 

Jupiter 9 36 37 

Saturn 10 16 2 

Uranus Unknown. 



Unknown. 



Unknown. 



Arago and Lardner's Astronomy. 



45 



THE TIME OF THE SIDEREAL REVOLUTIONS. 
D H M S 

Mercury 87 23 14 30 

Venus 224 16 41 27 

48 49 

18 27 





The Earth 365 5 

Mars 686 22 

Vesta 3 years 66 4 



Juno 4 " 128 

Ceres 4 " 220 2 

Pallas 4 " 220 16 

Jupiter 11 " 315 12 30 

Saturn 29 " 161 4 27 

Uranus 83 " 29 8 39 

ANNUAL PARALLAXES. 

Mercury 126° 14 

Venus 139 9 

The Moon s 27 1 

Mars 18 6 

Jupiter 9 59 

Saturn 5 42 

Uranus 2 55 

INCLINATION OF THE ORBIT TO THE ECLIPTIC. 

Mercury 7° 78 

Venus 8 76 

The Moon 5 71 

Mars 1 85 

Vesta 7 15 

Juno 31 05 

Ceres 10 62 

Pallas 34 60 



Jupiter 1 46 

Saturn 2 77 

Uranus 8tf 



INCLINATION OF THE AXIS TO THE ORBIT 

The Sun 82° 

Mercury " 



50 





(< 


a 


The Earth 


66 


r ><> 


The Moon 


88 


5(1 


Mars 


61 


r -sn 


Vesta 








> Unknown. 




Pallas 

Jupiter 


89 


4^ 


Saturn 


60 




Uranus 




u 



VELOCITY IN LEAGUES PER SECOND. ' 

Mercury 635 

Venus 485 

The Earth 412 

The Moon 14 (rel. to the Earth.} 

Mars 329 

Vesta 1 

ce?e 8 ';..:.'. c Unkn ° wn - 

Pallas ) 

Jupiter 177 

Saturn 132 

Uranu3 93 



LECTURE VIII. 



KEPLER'S LAWS.— UNIVERSAL ATTRACTION. 



KEPLER S LAWS. 

In treating of the planets, we have contented 
ourselves with saying, that they describe round 
the sun elliptic curves more or less elongated, 
but we have not yet inquired into the means of 
determining these orbits, nor have we studied 
their nature. 

An ellipsis is an oval. This figure differs 
from a circle, in being unequal in its diameters, 
and in having two points called its foci. 

The foci are the two points in the longest 

Fig. 31. 




axis of an ellipsis, on which as centres the figure 
is described, as s and e. 

The eccentricity of an ellipsis is the distance 
between the centre and either foci, as sc or ec. 

When the earth or any other planet is in that 
part of its orbit nearest the sun, it is said to be 
in its perihelion, as at a ; and when in that part 
farthest from the sun, as at b, it is said to be in 
its aphelion. The line sd represents its mean 
distance. 

The curves described by the planets all make 
angles greater or less with the plane of the 
ecliptic, consequently they all cut it in two ex- 
actly opposite points called nodes. The line 
joining these points is the line of the nodes: this 
line marks the intersection of the plane of the 
orbit with that of the ecliptic. 

Let us now suppose a spectator placed in the 
sun: it will be easy for him to distinguish the 
precise instant of the passage of the planet at its 
nodes; it will be when he sees it in the line 
passing through the node and the centre of the 
sun. As for the observer situated on the earth, 
that is to say, out of the centre of the planetary 
system, he can certainly mark the instant of the 
passage of the nodes, but he cannot see them 
when they are constantly opposed to each other, 
because the right line joining them assumes sue- 



46 



Arago and Lardner's Astronomy. 



eessively various inclinations in consequence of 
the sun's motion; it sometimes happens, how- 
ever, but very rarely, that the earth and the sun 
being in a line, the planet we wish to observe 
is also in the prolongation of the same line. The 
planet is then seen at the same point as the sun, 
its longitude can be ascertained, and several 
such observations will enable us to determine if 
the planet's node always corresponds to the 
same longitude seen from the sun. 

The node being known, to determine the in- 
clination, we wait till the sun's longitude is the 
same as the planet's, and then we find the lati- 
tude of the star, whence we deduce the inclina- 
tion of the plane of the orbit. 

Ttese data being obtained, to determine the 
nature of the curve, we measure the duration of 
an entire revolution, which is done by watching 
a point, one of the nodes for instance, and reck- 
oning the time that elapses between two succes- 
sive passages of the star through this point. 

When the duration of the motion has thus 
been obtained, nothing remains but to deter- 
mine, by means of the oppositions and conjunc- 
tions, the angular motion of the planet. 

When we have thus traced the orbits of the 
planets, we find — 

1. That the planets all move in ellipses, of 
which the sun occttpies one of the foci. 

2. That the motion is the more rapid the 
nearer the planet is to the sun, so that the radius 
vector always describes equal surfaces in a given 
time. 

3. That the squares of the times of revolution 
are to each other as the eubes of the major axes 
of the orbits. 

These are Kepler's three laws: they are the 
foundation of all astronomy. We shall presently 
see how they involve in them the general law of 
attraction. These interesting laws, tested for 
every planet, have been found so perfectly ex- 
act, that we do not hesitate to infer the distances 
of the planets from the sun from the duration of 
their sidereal revolution: and it is obvious that 
this mode of estimating distances possesses con- 
siderable advantages in point of exactness, for it 
is always easy to determine precisely the return 
of each planet to a point in the heavens, while 
it is very difficult to calculate directly its dis- 
tance from the 6un. 

UNIVERSAL ATTRACTION. 

The announcement of Kepler's laws, render- 
ing so great a service to astronomy by discover- 
ing the marvellous relations between the celes- 
tial motions, could not fail of exciting inquiry as 
to the causes that governed these movements. 
This discovery was reserved for the genius of 
Newton. We shall not repeat how he was con- 
ducted to it by reflecting on the cause which 
had made an apple fall at his feet, a cause whose 
operation he conceived the brilliant idea of ex- 
tending to the stars: neither shall we enter into 
the intricate and laboriously calculated details, 
by which he succeeded in establishing this gen- 
eral cause. We shall confine ourselves to an 
exposition of the consequences he deduced from 
Kepler's laws. 

From the law that the areas described by the 
radius vector are proportional to the times, 
Newton draws this conclusion, supported by 



calculation, that the force acting on the planets 
is directed toward the centre of the sun. 

From the law that the orbits of the planets 
are ellipses, of which the sun occupies one of 
the foci, he concludes, that the force acting on 
the planets is in the inverse ratio of the square of 
the distance of their centres from that of the sun. 

Lastly, from the law that the squares of the 
times of revolution are to each other as the cubes 
of the major axes of the orbits, he draws this 
consequence, that the force is proportionate to 
the mass. 

From all these results it follows that the sun 
is the centre of an attractive power, which acts 
in accordance with the laws we have just stated. 

Newton, who, setting out from the attraction 
exercised by the earth over the bodies on its 
surface, extended the operation of the same 
principle to the moon, was led to conclude from 
analogy, that, since the other planets also retain 
their satellites in their orbits, they must possess 
like the earth an attractive force, and that it can 
only be a force of the same nature that gives the 
sun the power to make all the other planets of 
his system circulate round him. 

Thus all the bodies that revolve round the sun 
are like him endowed with the power of attrac 
tion; and if we push the analogy further, we 
arrive at this general result now adopted in 
physics, and which might have been anticipated 
from the sphericity of the heavenly bodies, 
namely, that all the molecules of matter mu 
tually attract each other with a force direct!) 
proportioned to their mass, and inversely to the 
square of their distances. 

But as the force of attraction, if it existed 
alone, could only tend to unite all the globes in 
nature into a single mass, Newton supposed that 
the heavenly bodies received a primitive im 
pulse in a direct line, and that from the combi 
nation of these two forces arose the curvilinear 
orbit. 

To illustrate this, suppose the body A is pro 
jected in the direction of the right line ABX 




into free space, where it meets no resistance to 
weaken the impulse it has received, it will coa- 



Arago and Lardner's Astronomy. 



47 



tinue to move on for ever with the same veloci- 
ty and in the same direction. But if on arriving 
at B it is attracted by S, with a sufficient force 
perpendicular to its "line of motion, it will quit 
ihe straight line ABX, and will describe round 
S the circle BYTU. In order that the body 
should thus describe a circle, it is necessary that 
the projectile force should be equal to that 
which it would have acquired from gravity alone 
in falling through the semiradius of the circle. 
Thus, that the body on arriving at B should de- 
scribe the circle BYTU, it is necessary it should 
be attracted by S so as to fall from B to S, 
(equal to half the radius BS,) in the time it 
would take to go from B to X, by the sole force 
of the projectile impulse. A may represent a 
planet, and S the sun. 

But if while the projectile force is carrying 
the planet from B to b, the sun's attraction 
should make it fall from B to i, the force of 
gravitation would be proportionally greater than 
in the former case, and the planet would de- 
scribe the curve BC. On the planet's arriving 
at C, the attractive force, augmenting inversely 
.is the squares of the distances, would be greater 
than at B, and would make the planet fall still 
more, so as to describe the arcs BC, CD, DE, EF 
in equal times; the planet would therefore move 
much more rapidly than before ; accordingly it 
would acquire a greater tendency to fly off at 
the tangent Kk, or in other words a greater pro- 
jectile force, which would be sufficiently pow- 
erful to overcome the force of attraction, and to 
prevent the planet falling upon the sun, or even 
from moving in the circle Klmn. The planet 
would therefore increase its distance, following 
the course of the curve KLB, but its velocity 
would gradually decrease from K to B, as it had 
augmented from B to K, because the attraction 
of the sun would now operate in an opposite di- 
rection. Having come back to B, after having 
lost from K to B the excess of velocity it has ac- 
quired from B to K, it would obey the same 
forces and describe the same curve. 

A double projectile force balances a quadru- 
ple attractive force. Let us suppose for instance, 
that the planet at B has toward X double the im- 
pulse it had before, that is to say, that it passes 
from B to c in the time it before took to move 
from B to b : in that case it will require four 
times as great a force of gravity to retain it in 
its orbit, that is to say, a force capable of making 
it fall from B to 4, in the time the projectile force 
would carry it from B toe, otherwise it could not 
describe the curve BD as shown in the figure. 

•As the planets approach toward and recede 
from the sun at every revolution, some difficulty 
may be felt in conceiving how in the first case 
they do not approach more and more, till they 
come in contact with him, and in the second 
case how it is they do not recede from him never 
to return ; but this difficulty vanishes when we 
study the action of these forces, and their rela- 
tive intensity in the cases in question. The 
planet, we have said, impelled by a projectile 
force which would carry it from B to b in the 
time the sun would make it fall from B to 1, and 
subjected to the action of these two forces, de- 
scribes the curve BC. But when the planet ar- 
rives at K, how will those two forces act 1 KS 
being equal to the half of BS, the planet will be 



twice as near the sun ; the action of gravity will 
therefore be four times as great according to the 
principle already laid down : consequently, it 
will tend to make the planet fall from K to V in 
the same time as it tended to make it fall from 
B to 1 : but the projectile force tends to carry 
the planet in the same time from K to k, a dis- 
tance equal to twice Bb, as the figure shows ; 
this projectile force is therefore double that 
which it had at B. Now we have already said 
that a double projectile force always balances a 
quadruple attractive force ; the equilibrium of 
the two forces will therefore not be broken, 
and the planet will continue its course from K 
to L 3 in the direction resulting from the opera- 
tion of the two forces. When arrived again at 
B, it will again be submitted to the two forces 
that made it describe its orbit the first time, and 
as these forces will act with the same intensity 
as before, it will go on indefinitely describing 
the same curve. 

Such is the grand principle of universal at- 
traction. It is so exact, that no perturbation, 
no deviation, however slight, takes place, for 
which it does not account with the most rigid 
accuracy. Astronomers put such implicit faith 
in it, that when their observations do not coin- 
cide with the results of their calculations, they 
are more disposed to believe that the error arises 
from the neglect of some circumstances of the 
case, than to question the validity of the doctrine 
of attraction ; and in point of fact they always 
become aware at last of the cause of the error. 

OF THE MASSES OF THE PLANETS. 

To the principle of attraction, we are also in- 
debted for the means of arriving at a knowledge 
of the mass and the density of the sun and the 
planets, of which an account will be found in 
the table at the end of the volume. Since the 
velocity of satellites in their orbits depends on 
the attractive force of the planet round which 
they revolve, the masses of the planets may be 
inferred from the velocities of their satellites. 
If the planet has no satellite, its mass is deter- 
mined by the perturbation it produces. 

The mass and the volume once known, the 
density may be found at once, by dividing the 
former by the latter. 

Cavendish determined the mass of our globe 
by another method, but one still founded on the 
principle of attraction. He took a very slender 
thread not twisted, at the extremity of which a 
needle was suspended, so as to be sensitive to 
the slightest attraction. Near this needle he 
placed a ball of lead, which by its attraction 
caused the needle to perform oscillations, the 
duration of which he observed. Then compar- 
ing these oscillations with those of the pendu- 
lum resulting from terrestrial gravitations, he 
calculated the relative force of the leaden 
sphere's attraction to that of gravity, and thus 
found the proportion of the mass oi the leaden 
ball to that of the earth. 

We shall see by and by, when we come to 
speak of the earth, that attraction has furnished 
the means of ascertaining the earth's dimensions 
with an accuracy in vain to be hoped for from 
direct measurements. 

* The 16th century formed a memorable epoch 
in the progress of astronomical knowledge. At 



48 



Arago and, hardness Astronomy. 



its commencement, Copernicus, born at Thorn, 
in 1472 revived that system which bears his 
name, and which already among the ancients 
had been prornulged under the high authority 
of Pythagoras. Tke system of Ptolemy rooted 
in the minds of mankind, and receiving universal 
assent for thirteen centuries, was not easily over- 
turned. The simplicity of truth, however, urged 
by advocates such as Copernicus and his suc- 
cessors, at length extorted the reluctant assent 
of the world. Galileo, born about the middle 
of the 16th century, was its earliest and greatest 
advocate, and Kepler, whose birth followed soon 
after, seconded the efforts of his illustrious cotem- 
porary. In the struggle which attended the tran- 
sition from error to truth, and in the reluctance 
felt even by philosophers to displace the earth 
from its central position, while nevertheless the 
arguments in favor of the central character of the 
sun, appeared irresistible, a compromise was pro- 
posed by Tycho Brahe, an eminent Danish astron- 
omer, in which, while the earth was maintained 
still as the centre of the system, it was admitted 
that the sun was the centre round which the 
movements of all the planets, save the earth, took 
place ; but that the sun thus carrying all the 
planets with it, like so many satellites, moved 
annually round the earth as a centre. This sys- 
tem was destined to be short-lived, and found 
little favor among philosophers. Unsustained by 
the prestige of antiquity, which supported that 
of Ptolemy, and deprived of the simplicity and 
clearness of truth, which favored the reception 
of that of Copernicus, it was soon abandoned 
even by those who temporarily favored it. John 
Kepler, born at Weil, in 1571, was the assistant 
and pupil of Tycho, and happily lor the progress 
of knowledge, was intimately familiar with a 
vast mass of elaborate, and invaluable observa- 
tions, made by that philosopher. Among these 
the observations made upon the apparent motion 
of the planet Mars, especially attracted the at- 
tention of Kepler, who engaged in extensive 
calculations with a view to ascertain the exact 
distance of that planet from the sun. These in- 
vestigations, which were undertaken with a 
view of discovering some imaginary numerical 
harmony, led to much grander results than Kep- 
ler had contemplated, or looked for. In the 
history of the progress of knowledge, frequent 
are the examples which occur of the greatest 
discoveries resulting from inquiries after objects 
which are comparatively trifling, and sometimes 
altogether imaginary. Roemer, when trying to 
measure the velocity of one of Jupiter's moons, 
discovered the velocity of light. Bradley, when 
attempting to determine the effect of the earth's 
annual motion on the stars, discovered aberra- 
tion ; and in the present case, Kepler, indulging 
in vain and imaginary theories of the harmonies 
of number, fell upon one of the most magnifi- 
cent discoveries in astronomical science. He 
found that observations on Mars &. different po- 
sitions, gave results which indicated different 
distances from the sun : this appeared at first so 
absurd, and includible, that the astronomer sup- 
posed that some unaccountable errors were in- 
volved in his calculations. The motion of the 
planets was universally admitted to be circular 
and uniform, and that of Mars among the rest. 
How then could this be compatible with a 



changeable distance from the sun ? However 
this might be, Kepler was soon convinced that 
such was the fact, and adhering religiously to 
the established doctrine of circular motion, he 
conjectured that although Mars might revolve in 
a circle, yet that the sun was not in the centre 
of that circle, and therefore, that the distance 
might vary notwithstanding the circularity of 
the motion. But in order to justify this suppo- 
sition, it was necessary to find a place for the 
sun within the circle, but different from the cen- 
tre, which would account for all the observed 
variations of distances, and this Kepler found to 
be impracticable. He was thus driven to the 
conclusion, that the periodical path of Mars 
round the sun, could not be circular, and the 
question then arose, what was its form ? Having 
ascertained by his own observations, and those of 
Tycho, a variety of distances of Mars from the 
sun, in different directions, during his periodi- 
cal course, we may conceive Kepler laying 
down those distances on a plane, according to a 
determinate scale, and making as it were, a mo- 
del, or pattern of the orbit. By such a course he 
could not fail to be struck with its close resem- 
blance to an ellipsis, or oval, the place of the 
sun being one of the foci. The truth having 
thus once found entrance to his mind in the 
form of a conjecture, he would naturally have 
tried how different forms of ellipses would ac- 
cord with, and explain all the variations of posi- 
tion of the planet, with respect to the sun, and 
could not fail speedily to discover the real char- 
acter of the orbit. The turn of Kepler's mind 
toward the investigation of numerical harmo- 
nies, happily led him to the discovery of the 
other two magnificent laws, which bear his 
name : the equable description of areas, and the 
accordance between the squares of the periodic 
times, and the cubes of the distances. 

* The discoveries of Kepler were limited to the 
establishment of these celebrated laws as de- 
tached, and disconnected facts, recognized by 
observation in the solar system. Newton suc- 
ceeded in presenting them in a much higher, 
and more general point of view. He showed 
that the uniformity of the areas, swept over by 
the line connecting the planet with the sun,was a 
mere consequence of the fact that the sun was 
the centre of attraction on the planet, and to put 
this point beyond the possibilicy of doubt, or ca- 
vil, he demonstrated on the most incontroverti- 
ble mathematical principles, these two general 
propositions. 

* 1. If a body be attracted toward a fixed cen 
tre, and describe round that centre in conse- 
quence of that attraction, and an original pro- 
jectile impulse, any kind of orbit, the line con- 
necting that body with the centre of attraction 
will move over equal areas in equal times. 

* 2. If a body traversing any orbit, so move, 
that aline drawn from it to a certain fixed point, 
move over equal areas, in equal times, then 
that, point must be the centre of attraction, to 
which the body so moving is subjected. 

* The discovery of gravitation consisted, in 
showing that all masses of matter in the uni- 
verse reciprocally attract with forces, the inten- 
sity of which, at equal distances, is proportional 
to the masses of the bodies, and which with 
equal masses at different distances, is in tha 



Arago and Lardner s Astronomy. 



49 



inverse proportion of the squares of the distan- 
ces ; that is to say, at double the distance, it is 
ene fourth, and so on. This law was deduced, 
by Newton, from the elliptical form of the orbits 
and the harmony prevailing between the peri- 
odic times and the distances. 

* The character of Galileo, says Sir David 
Brewster, whether we view him as a member 
of the social circle, or as a man of science, pre- 
sents many interesting and instructive points of 
contemplation. Unfortunate, and to a certain 
extent immoral in his domestic relations, he did 
not derive from that hallowed source all the en- 
joyments which it generally yielded, and it was 
owing to this cause, perhaps, that he was more 
fond of society than might have been expected 
from his studious habits. His habitual cheer- 
fulness and gaiety, and his affability and frank- 
ness of manner, rendered him a universal favo- 
rite among his friends. Without any of the 
pedantry of exclusive talent, and without any of 
that ostentation which often marks the man of 
limited, though profound acquirements, Galileo 
never conversed upon scientific or philosophical 
subjects, except among those who were capable 
of understanding them. The extent of his 
general information; indeed, his great literary 
knowledge, but above all, his retentive memory, 
stored with legends and poetry of ancient times, 
saved him from the necessity of drawing upon 
his own peculiar studies for the topics of his 
conversation. 

Galileo was not less distinguished for his hos- 
pitality and benevolence ; he was liberal to the 
poor, and generous in the aid which he admin- 
istered to men of genius and talent, who often 
found a comfortable asylum under his roof. In 
his domestic economy, he was frugal without 
being parsimonious; his hospitable board was 
ever ready for the reception of his friends, and 
although he was himself abstemious in his diet, 
he seems to have been a lover of good wine, of 
which he received always the choicest varieties 
from the grand duke's cellar. This peculiar 
taste, together with his attachment to a country 
life, rendered him fond of agricultural pursuits, 
and induced him to devote his leisure hours to 
the cultivation of his vineyards. 



In his personal appearance, Galileo was about 
the middle size, and of a square-built, but well 
proportioned frame; his complexion was fair? 
his eyes penetrating, and his hair of a reddish 
hue; his expression was cheerful and animated, 
and although his temper was easily ruffled, yet 
the excitement was transient, and the cause of 
it speedily forgotten. 

One of the most prominent traits in the char- 
acter of Galileo, was his invincible love of truth, 
and his abhorrence of that spiritual despotism 
which had so long brooded over Europe. His 
views, however, were too liberal and too far in 
advance of the age which he adorned, and how- 
ever much we may admire the noble spirit 
which he evinced, and the personal sacrifices 
which he made in his struggle for truth, we 
must yet lament the hotness of his zeal, and the 
temerity of his onset. In his contest with the 
Church of Rome, he fell under her victorious 
banner, and though his cause was that of truth, • 
and her's that of superstition, yet the sympathy 
of Europe was not roused by his misfortunes. 
Under the sagacious and peaceful sway of Co- 
pernicus, Astronomy had effected a glorious 
triumph over the dogmas of the Church; but 
under the bold and uncompromising rule of 
Galileo, all her conquests were irrecoverably 
lost. 

The scientific character of Galileo, and his 
method of investigating truth, demand our 
warmest admiration. The number and inge- 
nuity of his inventions, the brilliant discoveries 
which he made in the heavens, and the depth 
and beauty of his researches respecting the 
laws of motion, have gained him the admiration 
of every succeeding age, and have placed him 
next to Newton in the lists of original and in- 
ventive genius. To this high rank he was 
doubtless elevated by the inductive process 
which he followed in all his inquiries. Under 
the sure guidance of observation and experiment, 
he advanced to general laws ; and if Bacon had 
never lived, the student of nature would have 
found, in the writings and labors of Galileo, not 
only the boasted principles of inductive philoso- 
phy, but also their practical application to the 
highest efforts of invention and discovery. 



LECTURE IX. 



THE EARTH 



The reason why, in our review of the planets, 
we have not spoken of the earth in its order of 
place is, that, in order to treat of it fully, we 
wished first to be in possession of indispensable 
preliminary notions. 

We shall speak successively of the figure, the 
dimensions, and the motions of the earth. 

FIGURE OF THE EARTH. 

Deceived by an illusion of the senses, men for 
a long while regarded the earth as a boundless 
plain, till observation gradually removed this 
error. It was remarked in the flat countries of 

4 



the east, on approaching elevated and distant 
objects, that at first only the summit was seen, 
afterwards the less lofty points, and finally the 
base. This phenomenon could not be the re- 
sult of local accidents, or special circumstances, 
for the same thing was observed in all direc- 
tions ; and it was the more strikingly so in pro- 
portion as the atmosphere was purer. Nay, it 
was observed at sea, and here it was still more 
conclusive, there being no inequalities or obsta- 
cles in this situation ; here all is level, and the 
surface of the sea must necessarily accord with 
the figure of the globe. Every one knows, in. 



50 



Arogo and Lardner's Astronomy. 



fact, that as often as a vessel recedes from the i< phers, might here be enumerated to prove the 
shore, its lower parts disappear first, then its | rotundity of the earth, had we sufficient room 
more elevated parts successively from below j and inclination to take up the reader's time with 

the relation of them; for a veiy little attention, 
and a very little observation in travelling either 
by sea or land, must soon convince any reflec- 
ting person that the earth is of a globular form. 
Indeed, there is not even one solitary appear- 
ance, either in the whole celestial sphere or 
throughout the surface of the earth, that seems 
in the slightest degree to favor the idea of the 
earth's being an extended plane, or of any other 
figure thau that of a globe. 

* The figure of the earth is not, however ? per- 
fectly spherical — both theory and experience 
have shown that it is very nearly an oblate sphe- 
roid, somewhat raised or elevated about the 
equatorial parts, and flattened or depressed 
about the poles, and the difference between the 
equatorial and polar diameters, according to the 
latest and most accurate measurements, is about 
26 miles, its mean diameter being about 7,920 
miles, and its circumference 24,880 miles. 



upwards, and lastly the tops of the masts ; mari 
ners arriving toward port, discover at first only 
the tops of the loftiest objects, and see the low- 
er parts only by degrees, as they approach near- 
er. Subsequently, the convexity of the globe 
has been superabuntly demonstrated, whether 
by the voyages of enterprising mariners, who, 
after sailing round the globe, have returned to 
the point whence they set out by a route oppo- 
site to that on which they had started ; or by 
astronomical observations, such as the circular 
form of the shadow cast by the earth on the 
moon's disk when the latter is eclipsed ; or, fi- 
nally, by operations serving to determine the 
dimensions of the earth, as also the direction of 
the plumb-line at various stations. 

* When a ship recedes from the land, a per- 
son on shore will first lose sight of the hull, 
then of the masts and lower parts of the sails, 
and lastly of the topsails, gradually from bottom 
to top ; and when a ship appi'oaches the land, a 
spectator on shore first discovers the upper parts 
of the masts and sails, and then by degrees the 
lower parts and the hull, in proportion as the 
vessel comes nearer to the shore. 

Fig. 33. 




*It will be plain by the figure that were the ship 
a elevated, so that the hull should be on a hori- 
zontal line with the eye, the whole ship would 
be visible instead of the topmast, there being no 
reason, except the convexity of the Earth, why 
the whole ship should not be visible at a, as 
well as at b. 

* In all these cases, the obstruction to the sight 
arises from the interposed water, on account of 
the universal convexity of the surface. 

* It has been well ascertained, that eclipses of 
the moon are occasioned by the earth's shadow 
upon the moon; but in all eclipses, notwith- 
standing the various positions of the earth, this 
shadow is always circular ; which is another 
proof that the earth is a globe. 

* Another decisive argument is derived from 
observing the altitude of the north polar star, 
after travelling north and south a considerable 
number of miles; and generally, in travelling 
any great distance toward the north, the north- 
ern stars appear more elevated as we approach 
them, and the southern stars more depressed as 
we recede from them toward the north. When 
travelling toward the south, the southern stars 
become elevated, and the northern depressed. 
Were the earth an extended plane, such chan- 
ges in the positions of the fixed stars could never 
take place. 

* Many other reasons, suggested by philoso- 



DIMENSIONS OF THE EARTH. 

Since the earth has sensibly the form of a 
sphere, if we knew the length of one of its de- 
grees, by multiplying it by 360 we should ob- , 
tain the measure of the circumference, 
and consequently the diameter, the 
surface, and the volume of the earth. 
Our task, therefore, is reduced to 
finding the length of a teiTestrial de- 
gree. Now, to arrive at this practi- 
cally, the following is the method pur- 
sued.: — A space is selected on the 
earth, such that the perpendiculars de- 
termined by the plumb-line at each 
extremity of this space correspond to 
two stars separated from each other by 
one degree, and thus a terrestrial de- 
gree is obtained. As it may be supposed, there is 
no reason why a space greater or less than a de- 
gree might not be selected, from which the ex- 
act measure of a degree might always be de- 
duced by a simple proportion. The remainder 
of the operation consists in measuring the base 
thus chosen, and this is done with incredible 
precision by trigonometrical methods, which we 
cannot here elucidate. 

This practical determination of the terrestrial 
degree has confirmed the flattening of the earth 
at the poles, and its dilatation at the equator. In 
fact, the degree, or the space which it is neces- 
sary to go over between two verticals to change 
a degree, is not the same in all latitudes : it is 
longer the more we approach the poles, it is at 
its minimum at the equator, which indicates 
very plainly a flattening at the poles, and not an 
increased convexity, as had at first been sup- 
posed by a strange mistake. 

The amount of this flattening, deduced from 
operations on the surface, is l-306th : that is to 
say, the polar diameter is shorter than the equa- 
torial by l-306th ; the projecting ring at the 
equator is about thirteen miles thick. These 
measures are obtained mathematically from the 
moon's motion, with much more precision than 
they can be determined by measurement of the 
earth. 

Gravitation enables U6 also to deduce them 



Arago and Lardner's Astronomy. 



to 



from the oscillations of the pendulum, which 
vary at different points of the globe, according 
to the force of gravity. 



The following are the 



toises each 

Semi-diameter of the equator.... 1435 leagues. 

" at the pole 1430 

taken at 45 deg... 1432 

Flattening 4.65 

Length of one degree of the meri- 
dian, taken at the mid-space be- 
tween the pole and the equator 25 

Quadrant of the meridian of Paris.. 2250.3 

The degree of the arc of the meridian, of 
which we have here given the measurement, 
was taken in the middle of the space separating 
the pole from the equator. From the measure- 
ment of the arc of the meridian traversing 
France from Dunkirk to Barcelona, and which 
has been prolonged as far as to the island of For- 
mentera, the following results have been de- 
rived : — 

The geographical league of France numbers 
twenty-live to the degree ; the sea league of 
France twenty, and contains 2850 toises ; each 
sea league is equivalent to three minutes of a 
terrestrial degree ; one third of a league is 
equivalent to a mile, or a minute of the equator: 
it is an English* or Italian mile ; the Spanish or 
Dutch league and the German mile are fifteen 
to the degree, the Swedish twelve, the Hun- 
garian ten, and the Russian werst is ninety to | 
the degree 

The' 

amounts to 25,790,440 square leagues (about 
148 thousand millions of French arpents), three 
fourths of which are occupied by the sea ; of | 
the remainder, scarcely one half is inhabited 
(about three millions of square leagues). 

In this amount of the dimensions of the earth, 
we have made no mention of the inequalities on 
its surface ; because, in point of fact, the high- 
est mountain may be regarded as insensible 
iu comparison with its volume, and the surface 
of the earth, notwithstanding the asperities it 
presents, may, relatively speaking, be consid- 
ered as infinitely smoother than the rind of an 
orange. 

THE EARTH'S MOTION. 

The sphericity of the earth being established, 
and its dimensions known, we shall next proceed 
to its motion. We shall first show that it turns 
upon itself, and then that it has besides a motion 
that carries it from point to point in space. 

DIURNAL ROTATION OF THE EARTH. 

The whole celestial sphere appears to us to 
turn round the earth in twenty-four hours: is 
this spectacle real or is it an illusion ? 

In the first place, if we compare the earth, we 
shall not say merely with the globes of our sys- 

* That is, the English geographical, or sea mile, of 
\yhich there are sixty to a degree of the equator; of Eng- 
lish statute miles there are sixty-nine and a half to a de- 
gree. French geographical leagues may therefore be con- 
verted into English statute miles by multiplying them, say 
roughly, by two and three-quarters, more accurately by 
S.78. The French metre is the 10,000,000th part of the 
quadrant of the meridian of Paris, and is equal to 39 .37079 
English inches, o: three feet three inches and a quarter 
roughly. 



tem, hut with the infinity of stars which, as we 
have seen, are nothing else than suns, at least a« 
large as ours, and probable centres of as many 
planetary systems, we must own that it is but 
an imperceptible point when contrasted with 
these enormous masses ; and it will, no doubt, 
appear monstrous, that an atom should be a cen- 
tre round which circulate so many immense 
globes. Our amazement will be vastly enhanced, 
if we think of the incredible velocity with which 
these bodies must move to describe in such brief 
times incommensurable circles ; and as this ve- 
locity must augment with the distance, it will 
be necessary to admit that the earth attracts all 
the stars with a foi-ce the greater the farther 
they are from it ; a supposition which is absurd. 

We must, therefore, abandon a notion which. 
would lead to such conclusions as these, and put 
the question to ourselves, whether this appa- 
rent revolution of the heavens may not be the 
effect of an illusion of our senses. Thus we 
shall be led to suppose the movement of the 
earth, and this supposition being admitted, the 
phenomena will be explained logically and. 
easily. • 

In reality, accompanying the earth in its rota- 
tion, we seem to ourselves to remain stationary, 
while the stars appear to us to move in the di- 
rection opposite to that we are following. In the 
same way, when seated in a carriage or in a ves- 
sel at sea, we fancy we see objects moving from 
us with the more speed in proportion as they 
are nearer to us : the illusion is in this case the 
stronger the greater the rapidity of the motion, 
and as the crew of the vessel does not feel the 
motion that carries it along, so we are insensi- 
ble to that of the earth, moving as it does with 
much more rapidity, and never encountering ob 
stacle or resistance. 

The rotary movement of the earth, thus ren- 
dered extremely probable by the natural and 
easy explanation it affords of the phenomena, 
and by the evident absurdity of the opposite 
opinion, it now remains that we prove it di- 
rectly. 

It has been asserted that if the earth turned, 
a body thrown up into the air ought to fall back- 
wards ; that a stone let fall from the top of a 
tower ought not to fall at the foot of the building, 
because the earth had moved during the time of 
the fall. This is an error: experiments have 
shown that a projected body partakes the motion 
of the projector. Thus a person on board ship 
throws a body up into the air and catches it 
again with facility, and therefore he thinks Lie 
throws it up vertically; whereas, seen from the 
shore, the body appears thrown obliquely up- 
ward and forward. Every one knows that a 
stone dropped from the mast of a vessel in fall 
sail falls at the foot of the mast, just as it would 
do if the vessel were at rest ; and that a bottle 
of water, inverted and suspended above the cab- 
in, leaks out, drop by drop, and fills another 
placed exactly underneath, though the vessel 
sails several feet in the time each drop takes to 
fall. 

Hut the case is still stronger, and we can even 
derive from it a mathematical proof of the earth's 
rotation. Of two bodies, describing iu the same 
time two circumferences at unequal distances 
from the axis of rotation, that which describes 



52 



Arago and Lardners Astronomy. 



the more distant, and consequently greater cir- 
cumference, must move with more rapidity than 
the other. Let us suppose, then, that a body be 
set at liberty from the top of a high tower. As 
the top of the tower, describing a greater curve 
than the base, since it is more distant than it 
from the axis of rotation, possesses a more rapid 
motion, it will communicate this rapidity to the 
body let fall, and this body will not take the di- 
rection of a plumb-line, but will deviate from it 
toward the east. This has been confirmed in 
the most satisfactory manner by experiment. 

Another proof of the earth's rotation has been 
derived from the transmission of light. Before 
examining it, we must first premise that light 
does not move instantaneously, but takes a cer- 
tain time to pass through space. 

Galileo sought to solve this problem experi- 
mentally : he had a lantern constructed with a 
moveable shade, which he could drop over it, so 
as instantaneously to intercept the light. With 
a lantern of this kind in his hand he ascended to 
the top of a mountain, while another person 
with a similar lantern stood upon an adjacent 
summit. Galileo had desired jhis person to 
drop the screen over his lantern the instant he 
lost sight of the light from that he himself held. 
He supposed that if light only moved progress- 
ively, some time would elapse between the in- 
stant when he dropped his own screen and that 
in which he should see the light of the other 
lantern disappear. But he was deceived ; the 
two lights disappeared simultaneously, whence 
he concluded that light is propagated instanta- 
neously. We shall see that this erroneous con- 
clusion was the result of his not having experi- 
mented on a sufficiently large scale. 

Let S be the sun, T the 
earth, J Jupiter at the mo- 
ment of opposition, and 'J at 
the moment of conjunction. 
If we observe two immer- 
sions of one of Jupiter's satel- 
lites, the one at opposition, 
the other at conjunction, and 
if we then repeat the obser- 
vation in the inverse order, 
that is, if we observe one im- 
mersion at conjunction and 
the other at opposition, the 
time elapsing between the 
first two immersions observ- 
ed will be longer than that 
between the two latter, and 
the difference will be 16' 26". 
Now this difference can only 
result from the time necessa- 
ry for the immei'sions to become visible ; that is, 
from the time necessary for the light to arrive 
from 'J to T ; or, in other words, 16' 26 v is the 
time required by light to traverse the great di- 
ameter of the terrestrial orbit, whose length is 
■one hundred and ninety-one millions of miles. 
Light moves, therefore, with a speed of about 
one hundred and ninety-two thousand miles per 
second. 

The progressive transmission of light being 
-thus established, letus deduce from it our demon- 
stration of the earth's rotation. 

If the earth is immovable, we ought not to see 
the stars at the moment thev arrive at the hori- 



Fig. 34. 




|j zon, or at the meridian^ but only after the time 
! required for the rays they emit to reach us. 

If, on the contrary, the earth turns, we ought 
I to see the stars the moment they arrive either at 
i the horizon or at the meridian ; for, in conse- 
quence of the rotary motion, the eye will fall 
into the line of the rays which had set out some 
time before from the stars, and which now ar- 
rive at the points of space traversed by our 
horizon. 

Now we do see the stars the instant of their 
arrival. The proof of this is that the culmina- 
tions of Mars, for instance, would be more or less 
advanced or retarded according as that planet 
approached or receded from us, if we did not 
see it the moment it arrived at the meridian ; 
but no appearance of the kind is noticed : the 
earth, therefore, must turn. 

The earth being about 25.000 miles in circum- 
ference, the different points of the equator de- 
scribe in twenty-four hours a circle of the same 
dimensions ; that is, about one-tenth of a league 
per second. It is the speed of a cannon ball. 

Since the earth turns, it is possessed, like all 
other bodies subjected to a similar movement, 
of a centrifugal force, the intensity of which ap : 
pears, both from experiment and calculation, 
to be in proportion to the squares of the veloci- 
ties : hence the centrifugal force is at its maxi- 
mum at the equator, and is nothing at the poles. 
The force of gravity will therefore be less at the 
equator than at the poles, and this is demon- 
strated by the difference in the vibrations of the 
pendulum at these two stations. But it must 
not be forgotten that this difference does not de- 
pend solely on the action of the centrifugal force, 
for we have seen that the distance from the cen- 
tre is greater at the equator than at the poles, 
and we know that gravity acts inversely as the 
square of the distances. 

We are now prepared to account for the rea- 
son why the poles are flatted while the equator 
is dilated. 

The earth, like all the planets, must primitive- 
ly have been fluid : this, at least, is the opinion 
which both theory and observation unite in con- 
firming, and which is generally admitted in the 
present day. This being premised, let us give 
the earth its rotary motion round AB. The 
molecules situated in the 
canal AB, that is to say, in 
the line of the poles, aro 
not actuated by any cen- 
trifugal force, and, conse- 
quently, lose nothing of 
th'eir weight: the molecu- 
les, on the contrary, that 
fill the canal BC, are sub- 
jected to the action of the 
centrifugal force, which, in 
some degree, neutralizes 
attraction ; they are, there- 
fore, proportionally light- 
er : a greater quantity of 
them will therefore be ne- 
cessary to maintain the equilibrium. 

It is easy to devise experiments, showing that 
the velocity of rotation produces a flattened 
spheroid like that of the earth. Take two strips 
of pasteboard, or other flexible material, bend 
them into circles and mount them upon an axis. 



Fig. 35. 




Arago and Lardner's Astronomy. 



53 



so that they may turn with it. Make them turn 
slowly by means of a wince on the end of the 
axis, they will not undergo any change of form ; 
but if you give them a rapid motion, their poles 
sink, and the circles bulge out laterally. 

ANNUAL MOTION OF THE EARTH. 

We have seen that the earth turns on its axis 
in 24 hours, and that the apparent revolution of 
the sphere is only an illusion of our senses. We 
have now to inquire whether the annual revo- 
lution of the sun is real, or whether this too is 
not an appearance caused by the earth's locomo- 
tion, for we have learned to "distrust the evidence 
of our senses. 

But first let us describe the motion of the sun. 
If we every day observe that body, we find that 
it advances every 24 hours about one degree to- 
ward the east. Now one degree corresponds to 
four minutes of time ; the sun, therefore, daily 
arrives four minutes later in the plane of the 
meridian, so that at the end of 90 days, he will 
arrive six hours later than the star with which 
he originally arrived in company. After 180 
days they will both be in the plane of the meri- 
dian at the same time, but the one will be in the 
superior meridian, the other in the inferior. 
La'stly, after 365 days and a quarter, they will 
both meet in the meridian at the same time. 
The line described by the sun in the course of 
this movement is the ecliptic, the plane of which 
is inclined to the equator 23° 28". The most 
elevated points of the ecliptic are called sol- 
stices, because the sun seems to stop in them ; 
aad the equinoxes, that is, the periods at which 
the days are equal to the nights, take place when 
the sun is on the plane of the equator, that is, 
twice a year. 

Such is the course the sun appears to take in 
the course of a year ; but is this movement real ? 
Is it not rather the earth that traverses the 
ecliptic, and gives rise to the appearances we 
notice ? 

And, firstly, if we judge by analogy, we shall 
find it much more natural to admit that the earth, 
which wants only the motion of revolution to 
take its place among the class of planets, is 
really endowed with such amotion, than to im- 
agine that the sun circulates round the earth 
with all his train of planets, in defiance of the 
laws of attraction. But the extreme probability 
of the earth's revolution is converted into the 
highest degree of certainty, when we derive 
from observation of the phenomena which this 
theory so naturally explains, demonstrations that 
remove every trace of doubt. 

How is it possible, indeed, upon the supposi- 
tion of the earth's being stationary, to account 
for the phenomena of the stations and retrogra- 
dations of the planets ? And what can be more 
natural than the explanation of these by the 
contrary hypothesis ? 

We have seen, in speaking of the planets, that 
these bodies appear to move sometimes from 
west to east, sometimes from east to west, and 
sometimes to remain stationary. Such are the 
phenomena. Now let us suppose that the earth 
moves along the ecliptic, and let us see what 
follows. Let S be the Sun, T the Earth, and M 
Pilars, for instance. The earth moving more 
rapidly than Mara, will be at T' when that planet 



Fig. 36. 




has only reached to M'. Mars will, therefore, 
in consequence of the illusion we have spoken 
of, appear to have retrograded toward M. But, 
when the earth arrives at T", the line it will 
have pursued, being inclined with relation to 
that traced by Mars, will not effect a greater 
parallel length than the latter. Mars will thea 
appear stationary. Lastly, when the earth comes 
to T'", the line it describes inclining still more, 
Mars will appear to advance. 

Such is, according to the hypothesis of the 
earth's motion, the natural and easy explanation 
of the phenomena of stations and retrogrades : 
it would be in vain to seek it from any other 
system. 

Bradley, in endeavoring to determine the annual 
parallax of the fixed stars, discovered that they 
are not motionless ; but that, during the time 
the earth takes to traverse her orbit, they ap- 
pear, such of them as are in the plane of this 
orbit, to describe right lines — such as are in a 
plane perpendicular to this orbit, to describe 
circles — and those in intermediate planes,, ellip- 
ses more or less elongated, according as they more- 
or less approach one or other of these positions. 
These are the phenomena of the aberration of 
light, from which we derive a new demonstra- 
tion of the earth's annual motion. 

Let us remember that light requires a certain 
time to reach us from the stars. This being pre- 
mised, let CA be a ray of light falling perpen- 
dicularly on the line BD. If the eye is at rest 
in A, it will see the object in the 
direction AC, whether the light 
is propagated instantly or by suc- 
cessive motion : but if the eye is 
in motion from B to A, and if light 
moves with a velocity which is 
to that with which the eye moves 
as CA to BA, it will pass from G 
to A while the eye moves from B 
to A. Now each particle of light 
that makes the eye discern tho 
object is at C when the eye is at 



Fie. 37. 




54 



Arago and hardness Astronomy. 



B : let us, therefore, join the two points, B and 
C, and suppose that the line CB is a tube, in- 
clined to the line BD, and of such a diame- 
ter that it can only admit one particle of light. 
It is evident the particle of light at C, which 
will render the object visible to the eye 
when it arrives at A, will pass through the tube 
BC, which accompanies the eye in its movement, 
preserving its inclination : but since the particle 
of light has arrived at the eye through the tube 
BC, the eye will see the object in the direction 
of this tube. If, instead of supposing the tube 
extremely small, we enlarge its axis, the parti- 
cle of light will still pass along this axis, if it is 
properly inclined. In the same way, if the eye 
moves from D to A, the tube CD must be inclined 
in the contrary direction. 

It follows from this, that if the earth moves, 
we do not see the stars in their real position, but 
a little in advance of it, and the difference be- 
tween their real and their apparent position is to 
the sine of their visible inclination to the plane 
of the ecliptic, as the velocity of the earth is to 
that of light. 

We can now understand that, the earth's mo- 
tion being admitted, it follows thatfthe fixed stars 
must present the phenomenon observed by Brad- 



ley : and the explanation we have just given of 
this phenomenon, otherwise inexplicable, consti- 
tutes the most convincing proof of the revolution- 
ary movement of our globe. 

The earth is, therefore, no longer for us the 
motionless centre round which the whole uni- 
verse gravitates : it is but a small planet of the 
solar system, obeying, like all the others, the 
laws of gravity. Its distance from the sun is 
95,000,000 miles in round numbers: its annual 
revolution occupies 365d5h 48' 49"; this is called 
its tropical year : but the time it takes to accom- 
plish its annual revolution, reckoning from a fixed 
star till it returns to it, is 365d 6n 9' 12" ; this is 
called its sidereal year. The rotation of the 
earth on its axis takes place in 24 hours, the 
length of the natural day. Its diameter is 7964 
miles. A poiut in the equator traverses, by 
reason of the rotation, about -^jths of a mile per 
second, and though the earth moves in the 
ecliptic with a speed of 19£ miles per second, 
its motion is less rapid almost by one-half than 
that of Mercury. The diameter of the earth's 
orbit is about 189 millions of miles. We shall 
not dwell longer on these details, which are 
fully set forth in the tables. 



LECTURE X. 



SECULAR AND PERIODICAL INEQUALITIES. 



Since all bodies mutually attract each other, 
in obedience to the laws we have already recog- 
nized, the globes of our system must mutually 
counteract each other in their course, and under- 
go a variety of perturbations. This actually oc- 
curs, and herein lies the peculiar triumph of the 
theory of attraction. There is not one of these 
derangements or perturbations, however exceed- 
ingly minute it may be, of which it does not 
give the most rigid account. 

The irregularities occurring in the motions of 
the planets and then' satellites, have received 
the name of inequalities. There are secular and 
periodical inequalities. It is not meant by this 
classification to infer that the former are not also 
periodical, but that they occur after very long 
periods, while the others are accomplished in a 
shorter space of time. 

These derangements are limited : there are 
certain bounds they cannot pass. Thus the 
curves described may be more or less irregular, 
may more or less approach toward, or recede 
from, the circular form, but the mean distance 
from the sun will never vary : the inclination of 
the axis to the orbit may undergo some varia- 
tions, but they will never exceed certain limits. 

We do not propose to speak here of any but 
the more remarkable inequalities of the moon 
and of the earth. 

INEQUALITIES OF THE MOON AND OF THE EARTH. 

When the moon is in conjunction, that is, when 
in the course of her revolution she becomes sit- 
uated between the sun and the earth, she is 



nearer the former body than in the opposite po 
sition, and the sun's attraction then acting with 
more intensity, the moon's distance from the 
earth becomes augmented. When, on the 
contrary, the moon is in opposition, that is to 
say, when the earth is between it and the 
sun, the latter, acting more strongly on the 
earth, causes it in its turn to recede from its 
satellite. At the quadratures the sun's action 
leaves the earth's to predominate. The imme- 
diate effect of these derangements is, to influ- 
ence the velocity of the moon's motion ; thus it 
is remarked the velocity diminishes from con- 
junction up to the first quadrature, and becomes 
accelerated from quadrature to opposition: the 
velocity then diminishes up to the second quad- 
rature ; and then augments again up to conjunc- 
tion. These inequalities are called variations. 

As the moon accompanies the earth in its mo- 
tion round the sun, and as the earth in the course 
of its revolution assumes a greater or less dis- 
tance from that luminary, it is plain that these 
variations in distance will modify the phenome- 
non we have just described. This new species 
of inequality is named the annual equation. 

We have already said, in treating of the moon, 
that its nodes move on the ecliptic from east to 
west, and pass through 19°. 3286 yearly, which 
makes an entire revolution in about eighteen 
years seven months and a half, or more exactly, 
in 6786.54919 days. This motion of the nodes 
of the moon's orbit, and the variations of its in- 
clination to the ecliptic, are owing to the action 
of the sun. In fact, when the moon in her revo- 



Arago and Lardner's Astronomy. 



55 



lution round the earth approaches the 
plane of the ecliptic, the attraction of the 
gun makes it descend, and thus hastens 
the moment when it will cut the plane of 
the ecliptic. Hence the retrograde mo- 
tion of the nodes, and the change of the 
orbit's inclination to the ecliptic. 

The attraction exercised by the earth 
upon the moon, varies according as the lat- / 
ter is in apogee or in perigee, and accord- / 
ingly allows more or less influence to the J'"* 
sun's attraction. Hence arise elongations / 
or contractions of the moon's orbit, irregu- I 
larities which are called cvections. 

But the most remarkable of these ine ! 
qualities is the precession of the equinoxes. 
The sun does not every year cross the 
equator in the same point. If on a cer- 
tain day he crosses the equator at ascertain 
point, on the same day in the next year 
he crosses it at another point, situated 
50". 103 west of the former, and thus arrives at 
the equinox 20' 33" before having completed 
his revolution in the heavens, or passed from 
one fixed star to another. Thus the tropical 
year, or the true year of the seasons, is shorter 
than the sidereal year. The precession of the 
equinoxes results from the solar attraction exer- 
cised with greater intensity upon the meniscus 
of the equator, and tending to make it fall into 
the plane of the ecliptic, from which it is kept 
off and maintained in its inclination by the mo- 
tion of rotation. Retrograding every year50".103 
to the west, the equinoxes make a complete rev- 
olution in 25,867 years. Thus (the first point of) 
Aries °f t which formerly corresponded to the 
vernal equinox, is now thirty degrees more to 
the west, though by a convention among astron- 
omers, it always answers to the equinox. 

The retrograde motion of the equinoctial 
points makes the axis of the earth describe, by 
means of a conical movement, a small circle, 
the diameter of which is equal to twice its in- 
clination to the ecliptic ; that is to say, 46° 56'. 
Let NZSVL be the earth : its axis is prolonged 
to the stars, and ends in A, the actual north pole 
of the heavens, which is vertical to N, the noi-th 
pole of the earth ; let EOQ be the equator, IZ 
the tropic of Cancer, and VR that of Capricorn; 
VOZ the ecliptic, and BOX its axis, which should 
be considered as immovable, because the eclip- 
tic always passes through the same stars. But 
as the equinoctial points retrograde in this plane, 
the axis of the earth SON is in motion upon the 
centre of the earth O, so as to describe the double 
cone NO>i and SOs, round that of the ecliptic 
BOX in the same time as the equinoctial points 
travel round this plane ; that is to say, in 25,867 
years; and in this long interval, the north pole 
of the earth's axis describes the circle ABCDA 
in the starry heavens round the pole of the eclip- 
tic, which rests motionless in the centre of the 
circle. The axis of the earth being inclined 
23° 28' to that of the ecliptic, the circle ABCDA. 
described by the north pole of the earth's axis 
produced to A is nearly 46° 56', or double the 
inclination of the earth's axis. Consequently 
the point A, which is at present the north pole 
of the heavens, and near a star of the second 
magnitude at the end of the tail of Ursa Minor, 
or the lesser Bear, must be quitted by the axis 



Fig. 38. 




of our globe, which, retrograding one degree in 
seventy-one years and two-thirds, will point di- 
rectly toward the star at B in 6447 years and 
three-quarters, and in double that time, or 12,895 
years and a half, directly toward the star or point 
C, which will then be the north pole of the 
heavens. The actual position of the equator 
will be changed to eOq ; the tropic of Cancer 
TZ into Vz, and that of Capricorn VR into vZ ; 
and the sun in the part of the heavens where it 
is now in the tropic of Cancer, and makes the 
longest days and the shortest nights in the north- 
ern hemisphere, will then be in the terrestrial 
tropic of Capricorn, where it will produce the 
longest nights and shortest days. This effect 
will not be brought about for 12,895 years, be- 
ginning from the point C, or if we count from A, 
not for 25,867 years, the period necessary for the 
northern pole to make a complete revolution, and 
arrive at the point vertically situated with re- 
spect to that in which it is at present. 

Bradley had already discovered the aberration 
of light, and was making new observations to 
confirm it, when he perceived that the axis of 
the earth was sometimes more, sometimes less 
inclined to the ecliptic, causing similar variations 
in the planes of the equator and the ecliptic, and 
that it described round the mean pole, taken as 
a centre, a small ellipse, the major axis of which 
subtends an arc of the celestial sphere of 20" 
•153, and the minor axis 15"-001. This ellipsis 
is described in the same time as the cycle of the 
moon, namely, in about eighteen years seven 
months. The period of this nutation being pre- 
cisely the same as that of the motion of the 
nodes, the two phenomena must necessarily be 
connected with each other. It is, ill fact, the 
attraction of the moon that produces the phe- 
nomenon of nutation, by acting more strongly 
on the equatorial regions than on the poles. 

Finally, besides the two inequalities we have 
just pointed out in the earth's motions, and 
which are the principal ones to which this planet 
is subject, we shall notice another rather impor- 
tant one, resulting from the combined influences 
of the planetary attractions: this is the gradual 
motion of the plane of the ecliptic through the 
heavens, and the secular diminution of its incli- 
nation to the equator, by a quantity equal, or 
nearly so, to 52"-1154 (about the hundredth of 



56 



Arago and Lardner's Astronomy. 



the precession, £" a year, 1' in 115 years, 1° in 
6900 years.) 

This change in the obliquity of the equator to 
the ecliptic is confirmed by the observations of 
ancient astronomers, and by calculation. We 
can convince ourselves of it by comparing the 
actual situation of the stars with respect to the 
ecliptic, to that which they occupied in the 
earlier times. Thus we find that those, which 
according to the testimony of the ancients were 
situated north of the ecliptic near the summer 
solstice, are now more advanced toward the 
north, and have receded from this plane; and 
that those, which were south of the ecliptic near 



the summer solstice, have approached this plane, 
that some have passed into it, and even beyond 
it, on their course northward. The contrary 
changes take place near the winter solstice. 

M. Laplace, however, has demonstrated that 
this diminution in the obliquity of the ecliptic, 
is not of a nature to go on always augmenting, 
but that a period must come when this move- 
ment will begin to slacken, and then cease en- 
tirely, after which it will begin again in the op- 
posite direction. In this way a balancing motion 
will take place, which can never exceed from 
one to three degrees. 



LECTUKE XI. 

COMETS. 



* For the civil and political historian the past 
alone has existence — the present he rarely ap- 
prehends, the future never. To the historian of 
science it is permitted, however, to penetrate 
the depths of past and future with equal clear- 
ness and certainty; facts to come are to him 
as present, and not unfrequently more assured 
than facts which are past. Although this clear 
perception of causes and consequences charac- 
terizes the whole domain of physical science, 
and clothes the natural philosopher with powers 
denied to the political and moral inquirer, yet 
foreknowledge is eminently the privilege of the 
astronomer. Nature has raised the curtain of 
futurity, and displayed before him the succession 
of her decrees, so far as they affect the physical 
universe, for countless ages to come; and the 
revelations of which she has made him the in- 
strument, are supported and verified by a never 
ceasing train of predictions fulfilled. He " shows 
us the things which will be hereafter," not ob- 
scurely shadowed out in figures and in parables, 
as must necessarily be the case with other reve- 
lations, but attended with the most minute pre- 
cision of time, place, and circumstance. He 
converts the hours as they roll into an ever pre- 
sent miracle, in attestation of those laws which 
his Creator through him has unfolded; the sun 
cannot rise — the moon cannot wane — a star can- 
not twinkle in the firmament without bearing 
witness to the truth of his prophetic records. 
It has pleased the " Lord and Governor" of the 
world, in his inscrutable wisdom, to baffle our 
inquiries into the nature and proximate cause of 
that wonderful faculty of intellect- — that image 
of his own essence which he has conferred upon 
us; nay, the springs and wheelwork of animal 
and vegetable vitality are concealed from our 
view by an impenetrable veil, and the pride of 
philosophy is humbled, by the spectacle of the 
physiologist bending in fruitless ardor over the 
dissection of the human brain, and peering in 
equally unproductive inquiry over the gambols 
of an animalcule. But how nobly is the dark- 
ness which envelopes metaphysical inquiries 
compensated by the flood of light which is shed 



upon the physical creation . There ail is har- 
mony, and order, and majesty, and beauty. 
From the chaos of social and political phe- 
nomena exhibited in humatt records — pheno- 
mena unconnected to our imperfect vision by 
any discoverable law, a war of passions and pre- 
judices governed by no apparent purpose, tend- 
ing to no apparent end, and setting all intelli- 
gible order at defiance — how soothing and yet 
how elevating it is to turn to the splendid spec- 
tacle which offers itself to the habitual contem- 
plation of the astronomer! How favorable to 
the development of all the best and highest 
feelings of the soul are such objects! The only 
passion they inspire being the love of truth, and 
the chiefest pleasure of their votaries arising 
from excursions through the imposing scenery 
of the universe — scenery on a scale of grandeur 
and magnificence, compared with which what- 
ever we are accustomed to call sublimity on our 
planet, dwindles into ridiculous insignificancy. 
Most justly has it been said, that nature has im- 
planted in our bosoms a craving after the dis- 
covery of truth, and assuredly that glorious in- 
stinct is never more irresistibly awakened than 
when our notice is directed to what is going on 
in the heavens. "Quoniam eadem Natura cupi- 
ditatem ingenuit hominibus veri inveniendi, quod 
facillime apparet, cum vacui curis, etiam quid 
in ccelo fiat, scire avemus; his initiis inducti 
omnia vera diligimus; id est, fidelia, simplicia, 
constantia ; turn vana, falsa, fallentia odimus."* 
* Among the multitude of appearances which 
succeed each other in their appointed order, and 
of the times and manner of which the perfect 
knowledge of the astronomer enables him to ad- 
vertise us, there are some which more power- 
fully seize upon the popular mind, as well by 
reason of their infrequency and the extraordi 
nary circumstances which attend them, as by 
the imaginary consequences with which igno- 
rance and superstition have in times past and 
present invested them. Among these, Solar 
Eclipses had a prominent place; but a still mora 

* Cic. de Fm Bon. et Mai. ii. 14. 



Arago and Lardner's Astronomy. 



57 



interesting position must be assigned to Com- 
ets. 

* It is well known tbat the solar system, of 
which our planet forms a part, consists of a num- 
ber of smaller bodies revolving in paths, winch 
are very nearly circular, round the great mass of 
the sun placed in the centre. These paths or 
orbits are very nearly in the same plane; that is 
to say, if the earth, for example, be conceived 
to be moving on a flat surface, extended as well 
beyond its orbit as within it, then the other 
planets never depart much above or below this 
plane. A spectator placed upon the earth keeps 
within his view each of the other planets of 
the system throughout nearly the whole of its 
course. Indeed there is no part of the orbit of 
any planet in which at some time or other it may 
not be seen from the earth. Every point of the 
path of each planet can therefore be observed; 
and although without waiting for such observa- 
tion its course might be determined, yet it is 
material here to attend to the fact, that the 
whole orbit may be submitted to direct observa- 
tion. The different planets, also present pecu- 
liar features by which each may be distinguished. 
Thus they are observed to be spherical bodies 
of various magnitudes: the surfaces of some are 
marked by peculiar modes of light and shade, 
which, although variable and shifting, still, in 
each case, possess some prevailing and perma- 
nent characters' by which the identity of the ob- 
ject may be established, even were there no 
other means of determining it. The sun is the 
common centre of attraction, the physical bond 
by which this planetary family are united, 
and prevented from wandering independently 
through the abyss of space. Each. planet thus 
revolving in a circle has the same tendency to 
fly from the centre, that a stone has when 
whirled in a sling. Why then, it will be asked, 
do not the planets yield to this natural tendency ? 
What enables them to resist it? To this ques- 
tion no satisfactory answer can be given; but 
the fact tbat the tendency is resisted, being cer- 
tain, the existence of some physical principle in 
which the means of such resistance resides is 
proved. As the tendency to fly off is directed from 
the centre of the sun, the opposing physical in- 
fluence must consequently be directed toward 
that centre. This central influence is what has 
been called gravitation. Although we are still 
ignorant of the nature or proximate cause of this 
force, and of its modus operandi, we have ob- 
tained a perfect knowledge of the laws by which 
it acts ; and this is all that is necessary or ma- 
terial to enable us to follow out its consequences. 
By virtue of this force of gravitation then, the 
planetary masses receive a tendency to drop to- 
ward the sun, which tendency equilibrates with 
the opposite tendency to fly away, produced by 
their orbitual motion. On the exact equilibrium 
of these two opposite physical principles, de- 
pends the stability of the system: if the centri- 
fugal tendency proceeding from the orbitual 
motion were in excess, the planets would fall off 
from the central body, and depart for ever into 
the depths of space; if, on the other hand, the 
central influence, or gravitation toward the sun, 
existed in excess, these bodies would gradually 
approach that luminary, and finally coalesre 
with his mass. 



* Besides these bodies, the greater part of which 
have been long known, and the motions of most 
of which have been in some degree understood 
even from remote antiquity, there is a still more 
numerous class of objects, whose appearances in 
the system were of such a nature as to defy the 
powers of philosophical inquiry, until these 
powers received that prodigious accession of 
force which was conferred upon them by the 
discoveries of Newton. Unlike planets, comets 
do not present to us those individual characters- 
above mentioned, by which their identity may 
be determined: none of them have been satis- 
factorily ascertained to be spherical bodies, nor 
indeed to have any definite shape. It is certain 
that many of them possess no solid matter, but 
are masses consisting entirely of aeriform or va- 
porous substances; others are so surrounded 
with this vaporous matter, that it is impossible, 
by any means of observation which we possess, 
to discover whether this vapor enshrouds within 
it any solid mass. The same vapor which thus 
envelopes the body (if such there be within it,) 
also conceals from us its features and individual 
character; even the limits of the vapor itself are 
subject to great change in each individual 
comet; within a few days they are sometimes 
observed to increase or diminish some hundred- 
fold. A comet appearing at distant intervals 
presents, therefore, no very obvious means of 
recognition. A like extent of surrounding vapor 
would evidently be a fallible test of identity; 
and not less inconclusive would it be to infer di 
versity from a different extent of nebulosity. 

* If a comet, like a planet, revived round the 
sun in an orbit nearly circular, it might be seen 
in every part of its path, and its identity might 
thus be established independently of any pecu- 
liar characters in its appearance. But such is 
not the course which comets are observed to 
take. These bodies usually are observed to rush 
into our system suddenly and unexpectedly from 
some particular quarter of the universe. They 
first follow in a straight line, or nearly so, the 
course by which they entered, and this course 
is commonly directed to some point not far re- 
moved from the sun. As they approach that 
luminary, their path becomes curved, at first 
slightly, but afterward more and more, the 
curve being concave toward the sun. Having 
arrived at a certain least distance from the cen- 
tre of our system, they again begin to recede 
from the sun, and as their distance increases, 
their path becomes less and less curved; until at 
length they shoot off in a straight course, and 
make their exit from our system toward some 
quarter of the universe wholly different from 
that from which they came. 

* We have stated that none of the planets de 
part much above or below the plane of the 
earth's orbit; it is quite otherwise with comets, 
which follow no certain law in this respect; 
some of them sweep the system nearly in the 
plane in which the planets move; others rush 
through it in curves, oblique in various degrees 
to this plane; while some move in planes per- 
pendicular to it. The planets also move round 
the sun all in one direction. Comets, on the 
other hand, rebel against this law. and move, 
some in one direction and forae in another. 

* So far theu as observation informs us, we are 



58 



Arago and hardness Astronomy. 



left to decide between two suppositions: 1. 
That the comet has entered the system for the 
first time; and that having swept behind the 
sun, it has emerged in a different direction, never 
to return: 2. That it moves in a large orbit, of 
which the sun is not the centre, but, on the con- 
trary? is placed very near the path of the body 
itself; that the comet is visible only in that part 
of its orbit which is in the immediate neighbor- 
hood of the sun, but is invisible throughout that 
large part, which perhaps extends, through 
depths of space, far beyond our most remote 
planet. If the latter supposition be adopted, it 
would follow that the same comet, after emerg- 
ing from our system, would, after the lapse of a 
certain time, return to it, and pursue the same 
path, or nearly the same path, round the sun as 
before. If then we find, after the lapse of a cer- 
tain time, a comet following the same path while 
visible, as a former comet was observed to fol- 
low, we infer that they also followed the same 
path during that much longer period in which 
they were beyond the sphere of our observation , 
and consequently we infer, with a high degree 
of probability, that the comets which thus fol- 
low precisely the same track, must be the same 
comet. We say with probability, because there 
is a possibility, although it be a bare possibility, 
that two different comets should move precisely 
in the same orbit. 

* Now, let us suppose that during the appear- 
ance of a comet, its path from day to day, or 
perhaps from hour to hour, is so carefully ob- 
served, that we could delineate it with a cor- 
responding degree of accuracy in any plan or 
model oi the system. This path would, as we 
have seen, form a very small fragment of its en- 
tire orbit; but if the nature of that orbit were 
known, the principles of geometry would also 
enable us to complete the curve. Thus, if a 
small arc of a large circle be traceu. upon paper, 
every one conversant with geometry will be 
able to complete the circle, even though he be 
not told with what centre the small arc was de- 
scribed, or with what length of radius. It is the 
same with other curves. Newton has proved 
that every mass of matter which is moved 
through the system, under the attracting influ- 
ence of the sun, must, by its motion, trace one 
or other of those curves called conic sections; 
and that the curve must be so placed, that the 
centre of the sun shall be in that point which is 
called its focus. Now, conic sections are of 
three kinds; the ellipse, which is a curve of oval 
form, such that a point moving on it would re- 
trace the same course every revolution. But 
the other two species (called the parabola and 
hyperbola,) consist of two branches diverging 
from their point of connection in two different 
directions, and proceeding in those directions 
without ever again reuniting. If a body (as it 
might do by the established law of gravitation) 
entered our system by one branch of such a 
curve, it would, after sweeping behind the sun, 
emerge by the other branch never to return. 
Thus it appears, that either of the two suppo- 
sitions which we have just made, would be 
compatible with a law of gravitation; and it is 
possible that some comets might move in ellip- 
ses, returning continually over the same path at 
stated intervals, while others, mos'ing in para- 



bolas or hyperbolas, entering our system for the 
first and only time, would emerge from it in 
another direction, and quit it for ever. It will 
perhaps be asked, if the orbits must be conic 
sections, with the sun in the focus, how is it that 
the planetary orbits are considered as circles? 
The fact is, the planetary orbits are not strictly 
circular, though very nearly so ; they are ellipses, 
which are so slightly oval, that, when exhibited 
in a drawing, they would not be perceived to 
be so, unless their length and breadth were ac- 
curately measured. The centre of the sun, also, 
is in their focus, and not in their centre; but 
owing to their slightly oval form, the distance 
of the focus from the centre is very inconsidera 
ble compared with their whole magnitude.* 

*On the appearance of a comet then, the first 
question which presents itself to the astronomi- 
cal inquirer is, whether the same comet has ever 
appeared before ? and the only means which he 
possesses of answering this inquiry is, by ascer- 
taining, from such observations as may be made 
during its appearance, the exact path it follows ; 
and this being known, to discover, by the prin- 
ciples of geometry, the nature of its orbit. If 
the orbit be found to be an ellipse, then the re- 
turn of the comet would be certain, and the 
time of the return would be known by the mag- 
nitude of the ellipse. If the path, on the other 
hand, should appear to be either a parabola or 
hyperbola, then it would be equally certain that 
the comet had never been before in our system, 
and would never return to it. 

* But a difficulty of a peculiar nature obstructs 
the solution of this question. It 6o happens that 
the only part of the course of a comet which can 
ever be visible, is a portion, throughout which 
the ellipse, the parabola, and bypei'bola so 
closely resemble one another, that no observa 
tions can be obtained with sufficient accuracy to 
enable us to distinguish one from the other. In 
fact, the observed path of any comet, while visi- 
ble, may indifferently belong to an ellipse, para- 
bola, or hyperbola. 

* There is, nevertheless, a certain degree of 
definiteness in the observed course of the body, 
which, although insufficient to enable us to say 
what the nature of the entire orbit may be, is 
still sufficiently exact to enable us to recognize 
any other comet, which moves, while visible, 
nearly in the same course. If then, after the 
lapse of a certain time, a comet should be found 
following that course, there would be a strong 
presumption that it is the same comet returning 
again to our system, after having traversed the 
invisible part of its orbit. This probability 
would be strengthened, if, on the two occasions, 
the body should present a similar appearance; 
although this is not essential to the identity, 
since, as has been stated, the same comet is ob- 
served to undergo considerable changes, even 
during a single appearance. 

* The time between the appearances of comets 
following nearly the same path being noted, 
the interval— the identity of the bodies being 
assumed — must either consist of a single period, 
or of two or more complete periods. The epoc-h 
which is usually taken as the commencement of 

* Even if the orbit were circular, with the sun in the 
centre, it would not be incompatibl with the law of 
gravitation. 



Arago and Larder' s Astronomy. 



a new revolution being the instant of time at 
which the comet is at its least distance from the 
sun. the place of the comet at that moment is 
called its perihelion. The period of a comet 
may, therefore, be defined to be the interval of 
time between two successive arrivals at its peri, 
helion. 

* Having succeeded in identifying the path of 
any two comets, we are then in a condition to 
predict with some degree of probability the time 
at which the next appearance may be expected. 
It is certain — providing that it be the same 
comet — that it will arrive at its perihelion after 
the same interval nearly : also that it may arrive 
at half the interval, or a third of the interval, or 
any other fraction corresponding to the possible 
number of unobserved appearances which may 
have taken place in the interval between those 
appearances from which its return has been pre- 
dicted. The times, therefore, at which the 
comet may be looked for with a probability of 
finding it, may without difficulty be predicted: 
and if it has been a conspicuous body in the 
heavens on the occasion of its former appear- 
ances, there is a probability that the whole in- 
terval between these appearances constituted 
but one period, and that no return of the comet 
had escaped observation. 

* Such are the circumstances which may have 
been conceived to have presented themselves 
when the idea first occurred of attempting to 
ascertain the identity of former comets, and to 
discover the means of predicting their future re- 
turn. The Principia of Newton, which laid the 
foundation of all sound astronomical science, had 
appeared soon after the middle of the seven- 
teenth century; and Halley, the contemporary 
and friend of Newton, had his attention natural- 
ly directed to the physical inquiries which that 
immortal book suggested. One of the most cu- 
rious and interesting of these questions was that 
to which we now allude. Halley, referring to 
the records of all former observers, with a view 
to obtain means of determining, so far as possi- 
ble, the course of former comets, succeeded in 
identifying one which he had himself observed 
in 1682, with comets which had appeared on 
several former occasions ; and found, that the in- 
terval between its successive returns was from 
75 to 76 years. This discovery has since been 
fully confirmed, and the comet has received the 
name of Halley's cornet. We now propose to 
lay before the reader the history of this cele- 
brated comet. 

*In retracing the history of a body of this na- 
ture so far as we can collect it from ancient 
chroniclers and historians, it is necessary to bear 
in mind that the terror which the appearance of 
comets inspired, had a tendency to produce an 
exaggeration of their effects. The propensity 
to ascribe to supernatural causes effects which 
the understanding fails to account for, has ren- 
dered comets peculiarly objects of superstitious 
terror. They have been accordingly regarded 
in past ages as the harbingers of war, pestilence 
and famine, and of all the greatest scourges 
which have visited the human race. But more 
especially they have presided at the birth and 
death of the most celebrated heroes. Thus, a 
conspicuous body of this kind appeared for seve- 
ral days succeeding the death of Julius Caesar, 



and was regarded as the soul of that illustrious 
person transferred to the heavens. Another 
was seen at Constantinople in the year of the 
birth of Mohammed. It is obvious, that under 
the influence of such powerful prejudices, the 
circumstances attending these appearances 
would naturally be amplified and exaggerated ; 
and the probability of exaggeration is increased 
by the fact that since science has shed its light 
upon the civilized world, these terrible objects 
have, in a great degree, disappeared, and comets 
have dwindled for the most part into very insig- 
nificant appearances. One of the ill consequen- 
ces of this exaggeration is, that it greatly in- 
creases the difficulty of identifying the bodies 
which have been described with those which 
have appeared in more recent times. In fact, 
we have little more to guide us than the epochs 
of the respective appearances ; and, antecedently 
to the fifteenth century, we possess absolutely 
no other evidence of the identity of these bodies 
except the record of their appearance at the 
times at which we know, from their ascertained 
periods, they ought to have appeared. Adopt- 
ing this test of identity, it would seem at least 
probable that the first recorded appearance of 
Halley's comet was that which was supposed to 
signalize the birth of Christ. It is said to have 
appeared for twenty -four days ; its light is de- 
scribed to have surpassed that of the sun ; its 
magnitude to have extended over a fourth part 
of the firmament; and it is stated to have oc- 
cupied consequently about four hours in rising 
and setting. 

* In the year 323, a comet appeared in the sign 
Virgo. Another, according to the historians of 
the Lower Empire, appeared in the year 399, 
seventy-five years after the last ; this last inter- 
val being the period of Halley's comet. 

* The interval between the birth of Mithridates 
and the year 323 was four hundred and fifty- 
three years, which would be equivalent to six 
periods of 75£ years. Thus, it would seem, that 
in the interim there were five returns of this 
comet unobserved, or at least unrecorded. The 
appearance in the year 3.99 was attended with 
extraordinary circumstances. In the Theatrum 
Cometarum of Lobienietski,, it is described as 
cometa prodigiosce magnitudinis, horribilis aspec' 
tu, comam, ad terram tisque demittere visus. The 
next recorded appearance of a comet agreeing 
with the ascertained period marks the taking of 
Rome by Totila in the year 550 ; an interval of 
151 years, or two periods of 75£ years, having 
elapsed. One unrecorded return must, there- 
fore, have taken place in this interim. The next 
appearance of a comet coinciding with the as- 
signed period is 380 years afterward, viz. in 
the year 930, five revolutions having been com- 
pleted in the interval. The next appearance is 
recorded in the year 1005, after an interval of 
a single period of seventy-five years. Three revo- 
lutions would now seem to have passed unre 
corded, when the comet again makes its appear 
ance in 1230. In this, as well as in former ap- 
pearances, it is right to state once more, that 
the sole test of identity of these comets with 
that of Halley, is the coincidence of the times of 
their appearances, as nearly as historical records 
enable us to ascertain, with the epochs at which 
the comet of Halley might have been expected 



60 



Arago and Lardner's Astronomy. 



to appear. That such evidence, however, must 
needs be imperfect will be evident, if the fre- 
quency of cometary appearances be considered ; 
and if it be remembered that hitherto we find 
no recorded observations, which could enable 
us to trace even with the rudest degree of ap- 
proximation the paths of those comets, the times 
of whose appearances raise a presumption of 
their identity with that of Halley. We now, 
however, descend to times in which more satis- 
factory evidence may be expected. 

* In the year 1305, one of those in which the 
comet of Halley may have been expected, a 
comet is recorded of remarkable appearance ; 
cometa horrendce magnitudinis visus est circa 

ferias Paschatis, quern secuta est pestilentia max- 
ima. Had the horrid appearance of this body 
alone been recorded, this description might 
have passed without the charge of great exag- 
geration; but when we find the Great Plague con- 
nected with it as a consequence, it is impossible 
not to conclude that the comet was seen by its 
historians through the magnifying medium of 
the calamity which followed it. Another ap- 
pearance is recorded in the year 1380, unaccom- 
panied with any other circumstance than its 
mere date. This, however, is in stiict accord- 
ance with the ascertained peiiod of Halley's 
comet. 

* We now arrive at the first appearance at 
which observations were taken, possessing suffi- 
cient accuracy to enable subsequent investiga- 
tors to determine the path of the comet : and 
this is accordingly the first comet, the identity of 
which with the comet of Halley, can be said to 
be conclusively established. In the year 1456, 
a comet is stated to have appeared of " unheard 
of magnitude ; " it was accompanied by a tail 
of extraordinary length which extended over 
sixty degrees (a third of the heavens,) and con- 
tinued to be seen during the whole of the month 
of June. The influence which was attributed to 
this appearance renders it probable that in the 
record there exists more or less of exaggeration. 
It was considered as the celestial indication of 
the rapid success of Mohammed II., who had 
taken Constantinople, and struck terror into 
the whole Christian world. Pope Calixtus 
II. levelled the thunders of the church against 
the enemies of his faith, terrestrial and celestial, 
and in the same Bull exorcised the Turks and 
the comets ; and in order that the memory of 
this manifestation of his power should be for 
ever preserved, he ordained that the bells of all 
the churches should be rung at midday, — a cus- 
tom which is preserved in those countries to our 
times. I must be admitted that, notwithstand- 
ing the terrors of the church, the comet pursued 
its course with as much ease and security as 
those with which Mohammed converted the 
Church of St. Sophia into his principal mosque. 

The extraordinary length and brilliancy which 
was ascribed to the tail upon this occasion, have 
led astronomers to investigate the circumstances 
under which its brightness and magnitude would 
be the greatest possible ; and. upon tracing back 
the motion of the comet to the year 1456, it has 
been found that it was then actually under the 
circumstances of position wish respect to the 
earth and sun most favorable to magnitude and 
splendor. So far. therefore, the results of as- 



[| tronomical calculation corroborate the records 
of history. 

*The next return took place in the year 1531. 
Pierre Appian, who first ascertained the fact, 
that the tails of comets are usually turned from 
the sun, examined this comet, with a view to 
verify his statement, and to ascertain the true 
direction of its tail. He made accordingly nu- 
merous observations upon its position, which, 
though, compared with the present standard of 
accuracy, they must be regarded as of a rude 
nature, were still sufficiently exact to enable 
Halley to identify this comet with that observed 
by himself in 1682. 

* The next return took place in 1607, when the 
comet was observed by the celebrated Kepler. 
This astronomer, on his return from a convivial 
party, first saw it on the evening of the 26th 
September ; it had the appearance of a star of 
the first magnitude, and, to his vision, was with- 
out a tail; but the friends who accompanied 
him having better sight, distinguished the tail. 
Before three o'clock the following morning the 
tail had become clearly visible, and had acquired 
great magnitude. Two days afterwards, the 
comet was observed by Longomontanus ; he 
describes its appearance, to the naked eye, to 
be like Jupiter, but of a paler and more obscure 
light ; that its tail was of considerable length, of 
a paler light than that of the head, and more 
dense than the tails of ordinary comets. He 
states, that on the 24th of September following, 
the comet was not apparent ; that on the 24th of 
October it was seen obscurely, and some days af- 
terwards disappeared altogether. 

* The next appearance, and that which was ob- 
served by Halley himself, took place in 1682, a 
little before the publication of the Pri?icipia. A 
comet of frightful magnitude had appeared in 
1680, and had so terrified all Europe, that the 
subject of our present inquiry, though of such 
immense astronomical importance, excited com- 
paratively little popular notice. In the interval, 
however, between 1607 and 1682, practical as- 
tronomy had made great advances; instruments 
of observations had been brought to a state of 
comparative perfection ; numerous observatories 
had been established, and the management of 
them had been confided to the most eminent as- 
tronomers of Europe. In 1682, the scientific 
world was, therefore, prepared to examine this 
visitor of our system with a degree of care and 
accuracy before unknown. It was observed at 
Paris by Lahire, Picard, and Dominique Cassini; 
at Dantzic, by Hevelius ; at Padua, by Monto- 
nari ; and in England, by Halley and Flamstead. 

*Iu 1686,_ about four years afterward, Newton 
published his Principia, in which he applied to 
the comet of 1680 the general principles of phy- 
sical investigation first promulgated in that work. 
He explained the means of determining, by geo- 
metrical construction, the visible portion of the 
path of a body of this kind, and invited astrono- 
mers to apply these principles to the various re- 
corded comets,— to discover whether some 
among them might not have appeared at differ- 
ent epochs, the future returns of which might 
consequently be predicted. Such was the effect 
of the force of analogy upon the mind of New- 
ton, that without awaiting the discovery of a pe- 
riodic comet, he boldly assumed these bodies to 



Arago and Lardner's Astronomy. 



61 



he analogous to planets in their revolution 
round the sun. 

* In the third book of his Principia, he calls 
them a species of planets revolving in elliptic 
orbits, of a very oval form, and even remarks an 
analogy observable between the order of their 
magnitudes and those of the planets. He says, 
— " As among planets without tails, those which 
revolve in less orbits, and nearer to the sun, are 
of less magnitude, so comets which in their peri- 
helia approach still nearer to the sun than the 
planets, are much less than the planets, that 
their attraction may not act too strongly on the 
sun. But," he continues, " I leave to be deter- 
mined by others the transverse diameters and 
periods, by comparing comets which return af- 
ter long intervals of time to the same orbits." 

* It is interesting to observe the, avidity with 
which minds of a certain order snatch at general- 
izations, even when but slenderly founded upon 
facts. These conjectures of Newton were soon 
after adopted by Voltaire : — " II y a quelque ap- 
parence," says he, in an Essay on Cornets, 
" qu'on counaitra un jour un certain nombre de 
ces autres planetes qui sous le nom de cometes 
tournent comme nous autour du soleil, mais il 
ne faut pas esperer qu'on les connaissent toutes." 

And again, elsewhere, on the same subject: — 

** Cometes, que l'on craint a l'egal du tonnere, 
Cessez d'epouvanter les peuples de la terre ; 
Baas une ellipse immense achevez notre cours, 
Remontez, descendez pres de l'astre des jours." 

* Extraordinary as these conjectures must have 
appeared at the time, they were soon strictly re- 
alized. Halley uudertook the labor of examin- 
ing the circumstances attending all the comets 
previously recorded, with a view to discover 
whether any, and which of them, appeared to 
follow the same path. Antecedently to the year 
1700, four hundred and twenty-five of these 
bodies had been recorded in history ; but those 
which had appeared before the fourteenth cen- 
tury had not been submitted to any observations 
by which their paths could be ascertained, — at 
least not with a sufficient degree of precision to 
afford any hope of identifying them with those 
of other comets. Subsequently to the year 
1300, however, Halley found twenty-four comets 
on which observations had been made and re- 
corded, with a degree of precision sufficient to 
enable him to calculate the actual paths which 
these bodies followed while they were visible. 
He examined with the most elaborate care the 
courses of each of these twenty-four bodies; he 
found the exact points at which each of them 
penetrated the plane of the earth's orbit ; also 
the angle which the direction of their motion 
made with that plane ; he also calculated the 
nearest distance at which each of them approach- 
ed the sun, and the exact place of the body 
when at that nearest distance. In a word, he 
determined all the circumstances which were 
necessary to enable him to lay down, with suffi- 
cient precision, the path which these comets 
must have followed while they continued to be 
visible. 

* On comparing their paths, Halley found that 
one which had appeared in 16G1, followed near- 
ly the same path as one which had appeared in 
1532. Supposing then these to be two succes- 
sive appearances of the same comet, it would 



I follow that its period would be 129 years; and 
i Halley accordingly conjectured that its next ap- 
I pearance might be expected after the lapse of 
I 129 years, reckoning from 1661. Had this con- 
I jecture been well founded, the comet must have 
j appeared abou tthe year 1790. No comet, bow- 
ever, appeared at or near that time following a 
similar path. 

*Iu his second conjecture, Halley was more 
fortunate, as indeed might be expected, since it 
was formed upon more conclusive grounds. He 
found that the paths of comets which had ap- 
peared in 1531 and 1606, were very nearly iden- 
tical, and that they were in fact the same as the 
path followed by the comet observed by him- 
self in 1682. He suspected, therefore, that the 
appearances at these three epochs were pro- 
duced by three successive returns of the same 
comet, and that consequently its period in its 
orbit must be about 752 years. 

* So little was the scientific world at this time 
prepared for such an announcement, that Halley 
himself only ventured at first to express his 
opinion in the form of conjecture; but after 
some further investigation of the circumstances 
of the recorded comets, he found three others 
which at lecst in point of time agreed with the 
period assigned to the comet of 1682, viz. those 
of 1305, 1380, and 1456.* Collecting confi- 
dence from these circumstances, he announced 
his discovery as the result of combined obser- 
vation and calculation, and entitled to as much 
confidence as any other consequence of an es- 
tablished physical law. 

* There were nevertheless two circumstances, 
which to the fastidious sceptic might be suppos- 
ed to offer some difficulty. These were, first, 
that the intervals between the supposed suc- 
cessive returns to perihelion were not precisely 
equal; and, secondly, that the inclination of the 
comet's path to the plane of the earth's orbit 
was not exactly the same in each case. Halley, 
however, with a degree of sagacity which, con- 
sidering the state of knowledge at the time, 
cannot fail to excite unqualified admiration, ob- 
served that it was natural to suppose that the 
same causes which disturbed the planetary mo- 
tions must likewise act upon comets ; and that 
their influence would be so much the more sen- 
sible upon these bodies because of their great 
distances from the sun. Thus, as the attrac 
tion of Jupiter upon Saturn was known to affect 
the velocity of the latter planet, sometimes re- 
tarding, and sometimes accelerating it, accord 
ing to their relative position, so as to affect its 
period to the extent of thirteen days, it might 
well be supposed, that the comet might suffer 
by a similar attraction an effect sufficiently great 
to account for the inequality observed in the in- 
terval between its successive returns ; and also 
for the variation to which the direction of its 
path upon the plane of the ecliptic was found to 
be subject. He observed, in fine, that as in the 
interval between 1607 and 1682 the comet pass- 
ed so near Jupiter that its velocity must have 
been augmented, and consequently its period 
shortened by the action of that planet, this pe- 
riod, therefore, having been only seventy-five 
years, he inferred that the following period would 

* The path of the comet of U36 was afterwards fuliv 
identified with that of loS-2, 



62 



Ar age and Lardner's Astronomy. 



probably be seventy-six years or upwards ; and 
consequently, that the comet ought not to be ex- 
pected to appear until the end of 1758, or the be- 
ginning of 1759. It is impossible to imagine any 
quality of mind more enviable than that which, ii. 
the existing state of mathematical physics, could 
have led to such a prediction. The imperfect state 
of mathematical science rendered it impossible 
for Halley to offer to the world a demonstration of 
the event which he foretold. " He, therefore," 
says M. de Pontecoulant, " could only announce 
these felicitous conceptions of a sagacious mind as 
mere intuitive perceptions, which must be re- 
ceived as uncertain by the world, however he 
might have felt them himself, until they could be 
verified by the process of a rigorous analysis." 

* The theory of gravitation, which was in its 
cradle at the time of Halley's investigations, had 
grown to comparative maturity before the period 
at which his prediction could be fulfilled. The 
exigencies of that theory gave birth to new and 
more powerful instruments of mathematical in- 
quiry : the differential and integral calculus was 
its first and greatest offspring. This branch of 
science was cultivated with an ardor and success 
by which it was enabled to answer all the de- 
mands of physics, and consequently mechanical 
.science advanced, pari passzt. Newton's dis- 
coveries having obtained reception throughout 
the scientific world, his inquiries and his theo- 
ries were followed up ; and the consequences of 
the great principle of" universal gravitation were 
rapidly developed. Among these inquhries one 
problem was eminently conspicuous for the or- 
der of minds whose powers were brought to 
bear upon it. One of the first and simplest re- 
sults of the theory of gravitation was, that if a 
single planet attended the sun (its mass being 
insignificant compared with that of the sun), that 
planet must revolve in an ellipse, the focus of 
which must be occupied by the centre of the 
sun ; but, if a second planet be admitted into 
the system, then the elliptic form of their paths 
round the sun can be preserved only by the sup- 
position, that the two planets have no attraction 
for each other, and that no physical influence is 
in operation, except the attraction of the solar 
mass for each of them. But the law of univer- 
sal gravitation is founded upon the principle, 
that every body in nature must attract and be at- 
tracted by every other body. Thus, the elliptic 
character of the orbit is effaced the moment a 
second planet is introduced. But let us remem- 
ber, that in this case each of the two supposed 
planets are in mass absolutely insignificant com- 
pared with the sun. The amount of attraction 
depending on the greatness of the attracting 
body, the intensity of the solar attraction of 
each of the planets must predominate enormous- 
ly over the comparatively feeble influence of 
their diminutive masses on each other. The 
tendency of the solar attraction to impress the 
elliptic form on the paths of those planets, must 
therefore prevail in the main; and although 
their mutual attraction, however feeble, cannot 
be wholly ineffective, their orbits will, in obedi- 
ence to the solar mandate, preserve a general 
elliptic form, subject to those very slight devia- 
tions, or disturbances, due to their reciprocal 
attraction. The problem to discover the na- 
ture aud amount of these disturbances ie one of 



paramount importance in astronomy, and has 
been called the " problem of three bodies ;" and 
its extension embraces the effects of the mutual 
gravitation of all the planets of the system upon 
each other. This celebrated problem presented 
enormous mathematical difficulties. A particu- 
lar case of it, which, from the comparative small- 
ness of the third body considered, was attended 
with greater facility, was solved by Euler, D'A- 
lembert, and Clairaut. This was the case in 
which the single planet, revolving round the sun, 
was the earth, and the third body the moon. 

* Clairaut undertook the difficult application of 
this problem to the case of the comet of 1682, 
with a view to calculate the effects which would 
be produced upon it by the attraction of the dif- 
ferent planets of the system ; and by such means 
to convert the conjecture of Halley into a dis- 
tinct astronomical prediction, attended with all 
the circumstances of time and place. The exact 
verification of the prediction would, it was obvi- 
ous, furnish the most complete demonstration of 
the principle of universal gravitation; which, 
though generally received, was not yet consider- 
ed so completely demonstrated as to be indepen- 
dent of so remarkable a body of evidence as the 
fulfilment of such a calculation would afford. 

' To attain completely the end pi'oposed, it was 
necessaiy to solve two very different classes of 
problems, requiring different powers of mind, 
and different habits of thought and application. 
The mathematical part of the inquiry, strictly 
speaking, consisted in the discovery of certain 
general analytical formulae, applicable to the case 
in question; which, when translated into ordi- 
naxy language, would become a set of rales ex- 
pressing certain arithmetical processes, to be ef- 
fected upon certain given numbers ; and when 
so effected would give as the final results, num- 
bers which woidd determine the place of the 
comet, under all the circumstances influencing 
it from hour to hour. The actual place of the 
body being thus determined, it became a simple 
question of practical astronomy, to ascertain its 
apparent place in the firmament, at correspond- 
ing times. A table, exhibiting its apparent place 
thus determined in the firmament for stated in- 
tervals of time, is called its Ephemeris; it is the 
final result to which the whole investigation 
must tend, and is that whose verification by ob- 
servation would ultimately decide the validity 
of the reasoning, and the accuracy of the com- 
putations. Clairaut, a mathematician and natu- 
ral philosopher, was eminently qualified to con- 
duct such an investigation, as far as the attain- 
ment of those general analytical formulae which 
embodied the rules by which the practical as- 
tronomer, and arithmetician might work out the 
final results ; but beyond this point, neither his 
habits nor his powers would conduct him. La- 
lande, a practical astronomer,, no less eminent in 
his own department, and who indeed first urged 
Clairaut to this inquiry, accordingly undertook 
the management of the astronomical and arith- 
metical part of the calculation. In this prodi- 
gious labor (for it was one of most appalling 
magnitude) he was assisted by the wife of an 
eminent watchmaker in Paris, named Lepaute, 
whose exertions on this occasion have deserved- 
ly registered her name in astronomical history. 
* It is difficult to convey to the reader who is 



Arago and Lardner's Astronomy. 



63 



not conversant with such investigations, an ade 
quate notion of the labor which such an inquiry- 
involved. The calculation of the influence of 
any one planet of the system upon any other, is 
itself a problem of some complexity and diffi 
culty; but still, one general computation, de 
pending upon the calculation of the terms of a 
certain series, is sufficient for its solution. This 
comparative simplicity arises entirely from two 
circumstances which characterize the planetary 
orbits. These are, that though they are ellipses, 
they differ very slightly from circles ; and though 
The planets do not move in the plane of the eclip- 
tic, yet none of them deviate considerably from 
that plane. But these characters do not, as we 
have already stated, belong to the orbits of com- 
ets, which, on the contrary, are highly eccentric, 
:um1 depart from the ecliptic at all possible an- 
gles. The consequence of this is. that the cal- 
culation of the disturbances produced in the 
cometary orbit by the action of the planets 
must be conducted, not like the planets, in one 
general calculation applicable to the whole or- 
bit, but in a vast number of separate calcula- 
tions ; in which the orbit is considered, as it 
were, bit by bit, each bit requiring a calcula- 
tion similar to that of the whole orbit of the 
planet. In fact, for a very small part of its 
course, we treat the comet as we would a planet ; 
making our calculations, and completing them 
nearly in the same manner; but for the next 
part we are obliged to enter upon a new calcu- 
lation, starting with a different set of numbers, 
but performing over again similar arithmetical 
operations upon them. When it is considered 
that the period of Halley's comet is about seven- 
ty-live years, and. that every portion of its course, 
ior two successive periods, was necessary to be 
calculated separately in this way, some notion 
may be formed of the labor encountered by La- 
lande, and Madame Lepaute. " During six 
mouths," says Lalande, " we calculated from 
morning till night, sometimes even at meals, the 
consequence of which was, that I contracted an 
illness which changed my constitution for the 
remainder of my life. The assistance rendered 
by Madame Lepaute was such, that without her, 
we never could have dared to undertake this 
enormous labor, in which it was necessary to 
calculate the distance of each of the two planets, 
Jupiter and Saturn, from the comet, and their at- 
traction upon that body, separately for every 
successive degree, and for 150 years." 

*These elaborate calculations havingbeen com- 
pleted, Clairaut, fearing that the comet would 
anticipate his announcement, presented his first 
Memoir to the Academy on the 14th November, 
1758. In this Memoir he was compelled to 

* The name of Mad. Lepaute does not appear in Clai- 
raut's Memoir ; a suppression which Lalande attributes to 
(he influence exercised by another lady to whom Clairaut 
Mas attached. Lalande, however, quotes letters of Clai- 
raut, in which he speakes in terms of high admiration, of 
•■ in savante calculatrice." The labors of this lady in the 
work of calculation (for she also assisted Lalande in con- 
Mructiiig his Ephemeridcs) at. length so weakened her 
sight, that she was compelled to desist. She died in 1788, 
while attending on her husband, who had become insane. — 
See the articles on Comets, written with considerable abil- 
ity, in the Companion to the British. Almanac for the 
year, 1833. They are understood to be the produc- 
tion of M<-, De Morgan, Secretary of the Astronomical 
Society. 



adopt the path of the comet upon its former ap- 
pearance, as determined by the observations of 
Appian. These, however, were made at a time 
when little attention was paid to comets ; and 
were made moreover without that consciousness 
on the part of the observer of their future impor- 
tance, which would doubtless have produced 
greater accuracy. In calculating the effect of 
the attraction of Jupiter and Saturn upon the 
comet, in its two periods between 1707 and 1682, 
and between the latter period and the expected 
return, Clairaut proceeded upon the supposition 
that the masses of these planets were each what 
they were then supposed to be. It has, how- 
ever, since appeared, that the estimates of these 
masses were incorrect, more especially that of 
Saturn. The planet Herschel being then un- 
known, its influence upon the comet was, of 
course, wholly omitted. Neither did Clairaut 
take into account the action of the Earth. En- 
cumbered with the disadvantages of precision in 
his data, he predicted, in his first Memoir, that 
the comet would arrive at its nearest point to 
the sun on the 18th of April, 1759 ; but he stated 
at the same time that the imperfection of some 
of the methods of calculation he was compelled 
to adopt, was such as to leave a possibility of 
his prediction being erroneous to the extent of 
a month. After presenting this Memoir he re 
sumed his calculations, and completed some 
which he had not time to execute previously. 
He then announced that the 4th of April would 
be the day of the comet's arrival at the nearest 
distance to the sun. 

* This wonderful astronomical prediction was 
accompanied by a circumstance still more re- 
markable and interesting than that which we 
have noticed in the conjectures of Halley as to • 
the disturbing effects of the planets upon the 
comet's period. Clairaut stated that there might 
be very many circumstances which, independ- 
ently of any error either in the methods or pro- 
cess of calculation, might cause the event to de- 
viate more or less from its predicted occurrence ; 
one of which was the probability of an undis- 
covered planet of our system revolving beyond 
the orbit of Saturn, and acting by its gravitation 
upon the comet. In twenty-two years after this 
time this conjecture was accurately fulfilled by 
the discovery of the planet Herschel, by the late 
Sir William Herschel, revolving round the sun 
one thousand millions of miles beyond the orbit 
of Saturn ! 

* In the successive appearances of the comet 
subsequent to 1456, it was found to have gradn 
ally decreased in magnitude and splendor. 
While in 1456 it occupied two-thirds of the fir- 
mament and spread terror over Europe, in 1607, 
its appearance, when observed by Kepler and 
Longomontanus, was that of a star of the first 
magnitude ; and so trifling was its tail, that Kep- 
ler himself, when he first saw it, doubted if it 
had any. In 1682 it excited little attention ex- 
except among astronomers. Supposing this de- 
crease of magnitude and brilliancy to be pro- 
gressive, Lalande entertained serious apprehen- 
sions that on its expected return it might escape 
the observation even of astronomers ; and thua 
that this splendid example of the power of sci- 
ence, and unanswerable proof of the principle of 
gravitation, would be lost to the world. ' It i* 



64 



Arago and Lardners Astronomy. 



not uninteresting to observe the misgivings of 
this distinguished astronomer with respect to the 
appearance of the body, mixed up with his un- 
shaken faith in the result of the astronomical in- 
quiry. " We cannot doubt," says he, "that it 
will return ; and even if astronomers cannot see 
it, they will not therefore be the less convinced 
of its presence ; they know that the faintness of 
its light, its great distance, and perhaps even bad 
w eather, may keep it from our view ; but the 
world will find it difficult to believe us ; they 
will place this discovery, which has done so 
much honor to modern philosophy, among the 
number of chance predictions. We shall see 
discussions spring up again in the colleges, con- 
tempt among the ignorant, terror among the peo- 
ple, and seventy-six years will roll away before 
there will be another opportunity of removing all 
doubt." 

* Fortunately for science, the arrival of the ex- 
pected visitor did not take place under such un- 
toward circumstances. As the commencement 
of the year 1759 approached, " Les Astrono- 
mes," says Voltaire, " ne se coucherent pas." 

*The honor, however, of the first glimpse of 
the stranger was not reserved for the possessors 
of scientific rank, nor the members of academies 
or universities. On the night of Christmas Day, 
1958, George Palitzch, of Prolitz, near Dresden, 
" a peasant," says Sir John Herschel, "by sta- 
tion, an astronomer by nature," first saw the 
comet. He possessed an eight-foot telescope, 
with which he made the discovery ; and the 
next day communicated the fact to Dr. Hoff- 
man, who immediately went to his cottage, and 
saw the comet on the evenings of the 27th and 
28th of December. An astronomer of Leipzic 
observed it immediately afterwards; "but," 
«ays M. de Pontecoulant, "jealous of his discov- 
ery, as a lover of his mistress, or a miser of his 
treasure, he would not share it, and gave him- 
self up to the solitary pleasure of following the 
body in its course from day to day, while his co- 
temporaries throughout Europe were vainly di- 
recting their anxious search after it to other 
•quarters of the heavens." At this time Delisle, 
a French astronomer, and his assistant, Messier, 
who, from his unwearied assiduity in the pur- 
suit of comets, received from Louis the Ffteenth 
the appellation of La Furet de Cometes ("the 
'Comet-ferret), had been constantly engaged for 
eighteen months in watching for the return of 
Halley's comet It would seem that La Caille, 
-and other French astronomers at that time, con- 
sidering that Delisle and Messier, from the at- 
tention which they had given to such objects, 
and more especially from the ardor and indefat- 
igable perseverance of the latter, could not fail 
to detect the expected body the moment it came 
within view, did not occupy themselves in look- 
ing for it. Delisle computed an Ephemeris, and 
made a chart of its supposed course in the heav- 
ens, and placed it in the hands of Messier to 
guide him in his search. This chart was errone- 
ous, and diverted the attention of Messier to a 
quarter of the firmament through which the 
comet did not pass, and thus, most probably, de- 
prived that zealous and assiduous observer of the 
honor of first discovering its return to our sys- 
tem. He succeeded, nevertheless, in observing 
it on the 21st of January, 1759"; nearly a month 



after it had been seen by Palitzch and Hoffman 
but without knowing that it had been already 
observed.* The comet was now observed in 
various places. It continued to be seen at 
Dresden, also at Leipzic, Boulogne, Brussels, 
Lisbon, Cadiz, &c. Its course being observed, 
it was found that it arrived at its perihelion, or 
at its nearest point to the sun, on the 13th of 
March, between three and four o'clock in the 
morning; exactly thirty-seven days before the 
epoch first assigned by Clairaut. but only twen- 
ty-three days previous to his corrected predic- 
tion. The comet on this occasion appeared very 
round, with a brilliant nucleus, well distinguish- 
ed from the surrounding nebulosity. It had, 
however, no appearance of a tail. About the 
middle of the latter month, it became lost in the 
rays of the sun while approaching its perihelion ; 
it afterwards emerged from them on its depart- 
ure from the sun, and was visible before sunrise 
in the morning on the 1st of April. On this day 
it was observed by Messier, who states that he 
was able to distinguish the tail by his telescope. 
It was again observed by hina on the 3rd, 15th, 
and 17th of May. Lalande, however, who ob- 
served it on the same occasions, was not able to 
I discover any trace of the tail. 

* Although it is certain that the splendor aud 
magnitude of the comet in 1759 were considera- 
bly less than those with which it had previously 
appeared, yet we must not lay too much stress 
upon the probability of its really diminished 
magnitude. In 1759 it was seen under the 
i most disadvantageous circumstances — it was al- 
j most always obscured by the effect of twilight, 
| and was in situations the most unfavorable pos- 
sible for European observers. It had been ob- 
served, however, in the southern hemisphere at 
Pondicherry by Pere Cceur-Doux, and at the isle 
of Bourbon by La Caille, under more favorable 
circumstances ; and both of these astronomers 
agree in stating that the tail was distinctly visi- 
ble by the naked eye, and varied in length at 
different periods from ten degrees to forty-seven 
degrees.t These circumstances are obviously in 
perfect accordance with the former appearances 
of the same body. 

*On its departure from the sun it continued to 
be observed until the middle of April, when its 
southern position caused the time of its rising to 
follow that of the sun ; consequently it ceased to 
be visible in the morning. By a further change 
in its position, however, it again appeared after 
sunset on the 29th, and Messier then describes it 



* An interesting memoir of Messier may be found in the 
Histoire de V Astronomie au dixhuitieme Siecle, by Delam- 
bre. La Harpe {Correspondence Litteraire. Paris, 1801, 
torn. i. p. 97) says, that " he passed his life in search of 
comets. The ne plus ultra of his ambition was to be made 
a member of the Academy of Petersburgh. He was an ex- 
cellent man, but had the simplicity of a child. At a time 
when he was in expectation of discovering a comet, his 
wife took ill and died. While attending upon her, being 
withdrawn from his observatory, Montagne de Limoges an- 
ticipated him by discovering "the comet. .Messier was in 
despair. A friend visiting him began to offer some consola- 
lation for the recent affliction he had suffered : Messier, 
| thinking only of his comet, exclaimed : — " I had discovered 
I twelve. Jilas, that I should be robbed of the thirteenth 
j by Montagne .'" and his eyes filled with teas. Then, 
J remembering that it was necessary to mourn for his wife, 
j whose remains were still in the house, he exclaimed. — 
j "Ah ! cette pauvre fe1nme, ,, and againwept for his comet " 
I t Memoires de l'Academie de» Sciences, 176(X 



Arago and Lardner's Astronomy. 



65 



as having the appearance of a star of the first 
maguitude. Bat here again unfortunately another 
circumstance interposed a difficulty — the light of 
the moon was at that time so strong as in a great 
degree to overcome the effect of the comet. The 
body disappeared altogether in the beginning of 
June. 

1 The comet had now commenced a new period 
under circumstances far more favorable than had 
ever before occurred. An interval of seven- 
ty-six years would throw its return into the 
year 1835. But during that interval, the sci- 
ence of analysis, more especially in its appli- 
cation to physical astronomy, has made prodig- 
ious advances. The methods of investigation 
have acquired greater simplicity, and have like- 
wise become more general and comprehensive ; 
and mechauical science, in the large sense of that 
term, now embraces in its formularies the most 
complicated motions and the most minute effects 
of the mutual influences of the various members 
of our system. These formulae exhibit to the 
eye of the mathematician a tableau of all the ev- 
olutions of these bodies in ages past, and of all 
the changes they must undergo (the laws of na- 
ture remaining unchanged) in ages to come. 
Such has been the result of the combination of 
transcendent mathematical genius and unexam- 
pled labor and perseverance for the last century. 
The learned Societies established in the vai'ious 
centres of civilization have more especially di- 
rected their attention to the advancement of 
physical astronomy : and have stimulated the 
spirit of inquiry by a succession of prizes offered 
for the solution of problems arising out of the 
difficulties which were progressively developed 
by the advancement of astronomical knowledge. 
Among these questions the determination of the 
return of comets, and the disturbances which 
they experience in their course, by the action of 
the planets near which they happen to pass, hold 
a prominent place. The French Academy of 
Sciences, in the year 1778, offered a high mathe- 
matioi prize for an essay on this subject, which 
was the means of calling forth the splendid Me- 
moir of Lagrange, which formed at once a com- 
plete solution and a model for all future investi- 
gations of the same kind. Lagrange's investiga- 
tion was, however, of a general nature, and it re- 
mained to apply it to the particular case of Hal- 
ley's comet, the only one then known to be pe- 
riodic. In 1820, the Academy of Sciences at 
Turin offered a prize for this application of La- 
grange's formula, which was awarded to M. 
Damoiseau. In 1826, the French Institute pro- 
posed a similar prize, having twice before offer- 
ed it without calling forth any claimant. On this 
occasion M. de Pontecoulant aspired to the hon- 
or. " After calculations," says he, " of which 
those alone who have engaged in such research- 
es can estimate the extent and appreciate the 
fastidious monotony, I arrived at a result which 
satisfied all the conditions proposed by the In- 
stitute. I determined the perturbations of Hal- 
ley's comet by taking into account the simulta- 
neous actions of Jupiter, Saturn, Uranus, (Her- 
schel,) and the earth ; the comet having passed 
in 1759 sufficiently near our planet to produce in 
it (the comet) sensible disturbances ; and I tlien 
fixed its return to its nearest point to the sun for 
the 7th of November, 1835." Subsequently to 

5 



this, however, M. de Pontecoulant made some 
further researches, which have led him to cor- 
rect the former result ; and he has since announ- 
ced that the time of its arrival at its nearest 
point to the sun will be on the morning of the 
14th November. 

* One of the circumstances, not the least sur- 
prising, connected with this comet is the magni- 
tude of its orbit. It is a very oblong oval, the 
total length of which is about thirty-six times 
the earth's distance from the sun ; and the great- 
est breadth about ten times that distance. The 
nearer extremity of the oval is at a distance 
from the sun equal to about half the earth's dis- 
tance ; and the more remote extremity at a dis- 
tance equal to thirty-five and a half times the 
earth's distance from the sun. The earth's dis- 
tance from the sun is, in round numbers, one 
hundred millions of miles ; the comet's least 
distance then will be fifty millions of miles, and 
its greatest distance three thousand five hundred 
and fifty millions of miles. Also, since the heat 
and light supplied by the sun to bodies which 
surround it diminish in the same proportion as 
the square of the distance increases, it follows, 
that at the nearest distance of the comet, the 
heat and light of the sun will be four times the 
heat and light at the earth, and at the greatest 
distance they will be about twelve hundred 
times less. Also the heat and light at the more 
remote extremity of the orbit, will be nearly 
five thousand times less than at the nearer ex- 
tremity ; so that while the sun seen from the 
comet will appear four times as large as it ap- 
pears at the earth at the nearer extremity, it will 
be reduced to the magnitude of a star at the 
more remote extremity. The vicissitudes of 
temperature, not to mention those of light, con- 
sequent upon this change of position, will be 
sufficiently obvious. If the earth were trans- 
ported to the more remote extremity of the 
comet's orbit, every liquid substance would be- 
come solid by congelation ; and it is extremely 
probable that atmospheric air and other perma- 
nent gases might become liquids. If the earth 
was, on the other hand, transferred to the near- 
er extremity of the comet's orbit, all the liquids 
upon it would be converted into vapor, would 
form permanent gases, and would either by 
their mixture constitute atmospheric air, or 
would arrange themselves into strata, one above 
the other, according to their specific gravities. 
All the less refractory solids would be fused, and 
would form in the cavities of the nucleus, oceans 
of liquid metal. 

* Besides the comet of Halley, there are two 
others, whose periodic returns have been ascer- 
tained. In the year 1818, a comet was observed 
at Marseilles, on the 26th of November, by M. 
Pons. In the following January, its path being 
calculated, M. Arago immediately recognized it 
as identical with one which had appeared in 
1805. Subsequently, M. Encke, of Berlin, suc- 
ceeded in calculating its entire orbit, — inferring 
the invisible from the visible part, — and found 
that its period round the sun was about 1200 
days. This calculation was verified by the fact 
of its return in 1822, since when the comet has 
gone by the name of Enckd's comet, and returned 
regularly at its appointed times in 1825, 1S29, 
and 1832. It will again arrive at i:s nearest 



66 



Arago and Lardner's Jisironomy. 



distance to the sun in the month of July in the 
present year. 

* On February 23th, 1826, M. Biela, an Austrian 
officer, observed iti Bohemia a comet, which 
was seen at Marseilles about the same time by 
M. Gambart. The path which it pursued was 
observed to be similar to that of comets which 
had appeared in 1772 and 1806. Finally, it was 
found that this body moved round the sun in an 
oval orbit, and that the time of its revolution 
was about six years and eight months. It has 
since returned, in the year 1832, at its predicted 
time ; and has been adopted as a member of our 
system, under the name of Biela's comet. 

* The orbit of Encke's comet is an oval, whose 
length is about double its breadth. At its near- 
est approach to the sun, the distance of the comet 
is about thirty-four millions of miles, which is 
about the distance of the planet Mercury. When 
most remote from the sun, its distance is about 
four hundred and forty-three millions of miles, 
which is nearly four and a half times the earth's I 
distance, and is little less than the distance of \ 
Jupiter. The orbit is inclined to that of the 
earth at nearly thirteen degrees. This comet 
may be considered as a planet, revolving within 
the orbit of Jupiter, and nearly in the commou 
plane of the solar system. Its motion, also, as 
well as that of Biela's, is in the same direction 
as that of the planets. 

* In the calculations of Encke for the determi- 
nation of the movement oi his comet, the most 
scrupulous account was taken of the effects 
which the planets must produce upon it. Nev- 
ertheless, a small discrepancy was found to ex- 
ist between its observed and computed returns 
in 1822, 1825, 1829, and 1832 ; and what was 
still more remarkable, this discrepancy was of 
the same nature in every case ; so that it is*im- 
possible to suppose that it could have arisen 
from any casual error of computation or of ob- 
servation ; since, had it so occurred, it would 
have affected the result irregularly. We must 
therefore conclude, that this comet does not pre- 
cisely retrace its steps each revolution. It is 
found, however, that this irregularity, from what- 
ever cause it may proceed, does not disturb the 
plane of the comet's path. It is, in fact, accord- 
ing to the observations and reasonings of Pro- 
fessor Encke, precisely the effect which would 
be produced if the space through which the 
comet moves was filled by a subtle fluid, offer- 
ing a»suiall resistance to the motion of the comet; 
just as our atmosphere resists the motion of any 
light body through it. 

* The existence of an extremely subtle ethereal 
Quid which fills the infinitude of space, has been 
idopted hypothetically to explain the phenome- 
na of optics. In fact, light itself is, according 
to the undulatory theory, supposed to consist in 
vibrations transmitted through such a fluid, just 
as sound is known to consist in similar undula- 
i ions transmitted through the atmosphere. Hith- 
erto this assumed cause for light has been justly 
regarded as an ingenious hypothesis not proved, 
out which accounts for the various phenomena 
more fully and satisfactorily than the corpuscu- 
lar theory; which, being open to the same ob- 
jection, completely fails when applied to some 
phenomena of light, which recent investigations 
have developed. If an effect similar to that 



which has been observed in Encke's comet 
should be discovered on the approaching return 
of Hailey's comet, and still more, if it be ob- 
served on the next return of Biela's comet,* the 
undulatory hypothesis will begin to assume the 
character of a vera causa ; and that theory oz 
light must, under such circumstances, be con- 
sidered as established. 

* The effect on the return of a comet produced 
by this resistance, contrary to what might at 
first be expected, is to accelerate it ; or to make 
the actual return anticipate the return as com- 
puted on the supposition that the comet moves 
in an unresisting medium, This difficulty will, 
however, be removed, if it be remembered that 
a resisting medium, by diminishing the velocity 
of the body in its orbit, diminishes the influence 
of the centrifugal force to resist solar attraction. 
The body, therefore, follows a path constantly 
nearer to the sun ; — in other words, the orbit 
is in a progressive state of diminution. Now, 
the less the orbit is, the less time necessary to 
describe it: and consequently the shorter the 
period of the successive returns of the body to 
the same position. 

* If the successive returns of the periodic com- 
ets should establish satisfactorily the existence of 
the luminous ether, it will follow that after the 
lapse of a certain time every comet will ulti- 
mately fall into the sun. In every succeeding 
revolution of the same comet, its path would 
fall a little within its former course, and it would 
describe a spiral line round the sun, continually 
approaching that body, until at length it would 
arrive close to its surface : before this could hap- 
pen, it would doubtless be wholly converted 
into a light gas by his heat, which would proba- 
bly mingle with the solar atmosphere. 

* In the efforts by which the human mind la- 
bors after truth, it is curious to observe how 
often that desired object is stumbled upon by 
accident, or arrived at by reasoning which is 
false. One of Newton's conjectures respecting 
comets was, that they are " the aliment by which 
suns are sustained ;" and he therefore concluded, 
that these bodies were in a state of progressive 
decline upon the suns, round which they re- 
spectively swept ; and that into these suns they 
from time to time fell. This opinion appears to 
have been cherished by Newton to the latest 
hours of his life : he not only consigned it to his 
immortal writings, but at the age of eighty-three, 
a conversation took place between him and his 
nephew on this subject, which has come down 
to us. " I cannot say," said Newton, " when 
the comet of 1680 will fall into the sun ; possi- 
bly after five or six revolutions ; but whenever 
that time shall arrive, the heat of the sun will 
be raised by it to such a point, that our globe 
will be burned, and all the animals upon it will 
perish. The new stars observed by Hipparchus, 
Tycho, and Kepler, must have proceeded from 
such a cause, for it is impossible otherwise 1o 
explain their sudden splendor." His nephew 
then asked him, " Why, when he stated in his 
writings that comets would fall into the sun, did 
he not also state those vast fires they must pro- 
duce, as he supposed they had done in the stars ? M 

* The last return of thi3 comet anticipated its calculated 
return by one day — Encke's comet loses two days cf its pe- 
riod every revolution. 



Arago and Lardner's Astronomy. 



67 



" Because," replied the old man, " the coufla- 1 
gratious of the sun concern us a little more di- 
rectly. I have said, however," added he, smi- 
ling, " enough to enable the world to collect my 
opinion." 

*It may be asked, if the existence of a resist- 
ing medium be admitted, whether the same ul- 
timate fate must not await the planets ? To 
this inquiry it may be answered, that within the 
limits of past astronomical record, the ethereal 
medium, if it exist, has had no sensible effect on 
the motion of any planet. That it might have 
a perceptible effect upon comets, and yet not 
upon planets, will not be surprising, if the ex- 
treme lightness of the comets compared with 
their bulk be considered. The effect in the two 
cases may be compared to that of the atmo- 
sphere upon a piece of swan's do^wn and upon a 
ieaden bullet moving through it. It is certain 
that whatever may be the nature of this resist- 
ing medium, it will not, for many hundred years 
to come, produce the slightest perceptible effect 
upon the motions of the planets. 

* Biela's comet moves in an orbit whose plane j 
is nearly the same with those of the planets, j 
It is but slightly oval, the length being to the 
breadth in the proportion of about three to two. 
When nearest to the sun, its distance is nearly 
equal to that of the earth ; and when most re- 
mote from the sun, its distance somewhat ex- 
ceeds that of Jupiter. Thus it ranges through 
the solar system, between the orbits of Jupiter 
and the Earth. 

* Excepting these three comets of Halley, 
Encke, and Biela, there is no other whose peri- 
odicity has been satisfactorily established ; that 
is to say, a prediction of whose return has been 
fulfilled. Dr. Olbers observed a comet in 18.15, 
whose return he has predicted in 1887. 

* The great comet of 1680 was conjectured to 
be identical with comets which had appeared 
in 1106, in 531, and in 43, B.C., the intervals be- 
ing 575 years. This conjecture, however, rests 
altogether upon the equality of the intervals of 
its appearance ; the path not having been ob- 
served antecedent to 1680. Should the conjec- 
ture be well founded, it cannot be verified un- 
til about the year 2255.* 

* Notwithstanding the discovery of the period- 
ic comets of Encke and Biela, still the comet of 
Halley maintains a paramount astronomical in- 
terest; and may be considered to stand alone in 
exhibiting those physical phenomena which | 
seem to be the exclusive characteristics of the | 
class to which it belongs. Although the comets j 
of Encke and Biela are unquestionably objects I 
of interest to the geometer and astronomer, yet I 
their short periods, the limited space within ! 
which they are circumscribed in their motion, | 
the small obliquity and eccentricity of their or- 
bits, and consequently the very slight disturb- 1 
mice which they sustain from the attraction of 
the planets, render them, for all physical pur- 
poses, nothing more than new planets of inap- 
preciable mass belonging to our system. Unlike 



* This is the comet to whose near approach to the earth 
Winston attributed the Deluge; the interval of time be- (I 
tween 1680 and the period assigned to the Deluge, either j| 
*\ the Hebrew or Septuagerian chronology, being very li 
nearly an exact multiple of the supposed period of the | 
•omet. il 



other known comets, they do not rush from the 
invisible and inaccessible depths of space, and, 
after sweeping our system, depart to distances 
under the conception of which the imagination 
itself is confounded. They possess none of that 
grandeur which is connected with whatever ap- 
pears to break through the fixed order of the 
universe. It is still reserved for the comet of 
Halley alone to exhibit a phenomenon, so far as 
we know, unique ; — to afford a splendid result 
of those powers of calculation by which we are 
enabled to follow it through the depths of space, 
two thousand millions of miles beyond the ex- 
treme verge of the solar system ; and, notwith- 
standing disturbances which render each suc- 
ceeding period of its return different from the 
last, to foretell that return with precision. 

* By far the greater number of comets appear 
to be mere masses of vapor, totally divested of 
all concrete or solid matter. So prevalent is 
this character, that some observers hold it to be 
universal. Seneca mentions the fact of stars 
having been distinctly seen through comets. A 
star of the sixth magnitude was seen through 
the centre of the head of the comet of 1795, by 
Sir William Herschel ; and in September, 1832, 
Sir John Herschel, when observing Biela's 
comet, saw that body pass directly between his 
eye and a small cluster or knot of minute tele- 
scopic stars of the sixteenth or seventeenth mag- 
nitude. This little constellation occupied a 
space in the heavens, the breadth of which was 
not the twentieth part of the breadth of the 
moon ; yet the whole of the cluster was distinct- 
ly visible through the comet. " A more striking 
proof," says Sir John Herschel, " could not have 
been offered of the extreme translucency of the 
matter of which this comet consists. The most 
trilling fog would have entirely effaced this group 
of stars, yet they continued visible through a 
thickness of the comet matter, which, calculat- 
ing on its distance and apparent diameter, must 
have exceeded fifty thousand miles, at least, to- 
ward its central parts." It is plain, therefore, 
that in this case, whatever may be the nature of 
this substance, it possesses no perceptible power 
either of absorbing or refracting the light which 
passes through it ; aud therefore, according to 
all probability, is of a density bearing a propor- 
tion which, in popular language, may be said to 
be infinitely small compared with the density of 
atmospheric air. " If any man should asset!; 
that the largest comet ever seen, including its 
millions of miles of tail, contained no more mat- 
ter than is to be found in the New River Head. 
he might justly be blamed for asserting more 
than he knew. But certainly any one who 
would positively deny the fact, would deserve 
the same censure."* 

* Nevertheless, M. Arago leans to the opinion, 
that some of the comets which have appealed 
have a solid nucleus within the nebulous matter 
which surrounds them. This opinion he grounds 
upon the intense splendor which has been im- 
puted to several of the recorded comets — such, 
for example, as in that which appeared in the 
year 43 B.C., and which the Romans considered 
to represent the metamorphosis of the eoul of 
Ca>sai. This was said to be visible in the prea- 

* Mr. Do Morgan, in the a*tioles alrc~>i\ cited. 



68 



Arago and Lordners Astronomy. 



ence of the sun. In 1402, another comet ap- 
peared, so brilliant, that the light of the sun. in 
the month of March, not only did not prevent 
the nucleus, but even the tail from being seen. 
We should attach to this example greater impor- 
tance, but for the latter part of the statement. 
"Whatever doubt there may be respecting the 
solidity of the matter forming the nucleus of 
Borne comets, there can be none respecting the 
tail ; and it does appear to us something little 
less than incredible that the tail of any comet 
could have been seen in the presence of the sun. 
On the whole, however, M. Arago's inference 
is, that while there are many comets without any 
nucleus, there are some with a nucleus which 
perhaps may be transparent ; and others more 
brilliant than planets, having a nucleus which is 
probably solid and opaque. The comets which 
are most intimately connected with our system — 
those of Encke and Biela — are mere masses of 
vapor, totally divested of solidity, and so small 
and faint, that they are not at all discoverable by 
the unassisted sight, and frequently cannot be 
detected without considerable difficulty even 
with telescopic aid. In 1832, Sir John Herschel, 
with the aid of a reflecting telescope of twenty 
feet in length, and possessing an enormous illu- 
minating power, could barely see Biela's comet ; 
and he asserts that if he had not discovered its 
position by such means, he would have found it 
quite impossible to have deleted it with a re- 
fracting telescope, although ne did see it after- 
wards with an equatorial instrument of that 
kind. 

* The extreme lightness of comets, compared 
with the smallest masses of the solar system, — 
as, for example, the new planets and the satel- 
lites of the old ones, — is fully established by 
the observed fact, that on their nearest approach 
to these bodies they never, by their attraction, 
cause them to deviate in the slightest perceptible 
degree from their usual course ; yet this cannot 
be accounted for by denying to the comets the 
quality of gravitation, since the attraction of the 
planets upon them is very considerable. In the 
year 1767 a comet, previously unknown, entered 
our system by a course so near the planet Jupi- 
ter, that the attraction of that body threw the 
comet completely into a new orbit; which was 
found by calculation, made by Lexell on the ob- 
servations of Messier, to be an oval or ellipse, 
in which, had the comet continued to move, its 
period would have been about five years and a 
half. While passing round the sun the comet 
followed this orbit, but on receding from the 
sun it passed, in 1779, among the satellites of 
Jupiter, and was again thrown into another or- 
hit by the attraction which it suffered, and was 
never afterwards seen. This circumstance, which 
was not understood at the time, occasioned con- 
siderable difficulty to astronomers ; but the pro- 
blem has since been solved by the methods 
given by Laplace ; and it has been ascertained 
that, previous to 1767, the comet moved in an 
orbit in which its period must have been at least 
fifty years, and at its nearest approach to the sun 
its distance would have been about six times 
the earth's distance. In such an orbit it is im- 
possible the comet would e\ er have been visible. 
The next disturbance of Jupiter, in 1779, threw 
it into a new orbit, in which its period would 



have been twenty years, and its least distance 
from the sun four times the earth's distance. 
Consequently, in such an orbit it never could be 
visible from the earth. In this case not the 
slightest effect was produced upon the motion of 
Jupiter's satellites by the attraction of the comet; 
from whence we must infer that the mass of the 
comet must have had an infinitely small propor- 
tion to the mass of the smallest of the satellites. 

* It is an interesting and well-ascertained fact, 
so far as any evidence can be collected from the 
periodic comets, that these bodies are undergo- 
ing a gradual decrease of magnitude. This has 
been particularly observable in the successive 
returns of Halley's comet ; in which, from its 
very long period, such an effect might be ex- 
pected to be conspicuous. But in the comets of 
Biela and Encke, of shorter periods, a like effect 
has been observed. The inference which must 
be drawm from this is, that the constituent parts 
of comets-are gradually scattered through space: 
possibly the formation of their tails, by the ope- 
ration of the sun, may expel matter from their 
masses, which the gravitation of the mass does 
not possess sufficient coercion to recall. Unless, 
however, we admit that a period will come 
when comets will altogether vanish from our 
system, we can scarcely attribute this declension 
of magnitude and splendor to comets universal- 
ly ; if they have a decay, they must have a 
growth ; if there be a decrease, there must be 
an increase, and a maximum ; otherwise, on 
tracing back such effects, we must, by assuming 
a sufficient duration of time, find a set of bodies 
of infinite magnitude and infinite splendor. 

* May it not happen, that in their excursions 
through the abyss of space, they may be fed 
with cometic matter, so that the waste of indi- 
vidual comets may be repaired ? Under certain 
circumstances, comets, whose courses may inter- 
sect, may coalesce ; — a larger may attract and 
cany with it a smaller. However this may be, 
we are not warranted in hastily generalizing the 
fact of the decay of magnitude obser-ved in the 
cases just mentioned. It is true that in the five 
last appearances of Halley's comet, its magni- 
tude and splendor appear to be on the decline. 
But if we apply the same reasoning to appear- 
ances antecedent to 1456, how, it may be asked, 
did its return so little attract the notice of his- 
torians in 1380 ? Also, between the year 1305 and 
399, although some returns are mentioned which 
correspond in time with the period of Halley's 
comet, yet we have no account of the same ter- 
rific object. The spirit of the times was never- 
theless such, that had it so appeared, it could 
scarcely have passed without exciting the usual 
superstitious terrors. Must we not then admit 
the possibility" of growth or increase as well as 
decline and diminution ? 

* It is a curious, and not uninteresting circum- 
stance, that the periodical path of Biela's comet 
passes very close to that of the earth ; so close, 
that at the moment the centre of the comet is 
at the point nearest to the earth's path, the mat- 
ter of the comet extends beyond that path, and 
includes a portion within it. Thus, if the earth 
were at that point of its orbit which is nearest 
to the path of the comet, at the same moment 
that the comet should be at that point of its or- 
bit which is nearest to the path of the earth, the 



Arago and Lardner's Astronomy. 



69 



earth would be enveloped in the nebulous at- 
mosphere of the comet. As this comet has no 
nucleus or solidity, a collision in such a case 
would, of course, be out of the question. The 
effect produced would be merely au interinix- 
ture of the cometie atmosphere with that of the 
earth. * The extreme light mass of the comet 
would, notwithstanding its proximity, render it 
impossible that it couid produce any sensible 
effect, either on the annual or diurnal motion of 
the earth ; so that our years, seasons, and days, 
would remain unchanged. With respect to the 
effect which might be produced upon our atmo- 
sphere by such a circumstance, it is impossible 
to offer anything but the most vague conjecture. 
We have already shown that the nebulous mat- 
ter of this comet must be infinitely more atten- 
uated than our atmosphere ; sp that the two 
fluids, when mixed, would be combined in a 
proportion in which our atmosphere would pre- 
vail to the extent perhaps of millions to one. 
For a single particle, therefore, of the cometary 
matter which we should inhale, we should in- 
spire millions of particles of atmospheric air. 
Under such circumstances, it is scarcely proba- 
ble that we should be conscious of the presence 
of the cometie matter at all. But even against j 
the occurrence of such a circumstance as this, 
there are many thousand chances. It is certain 
that every year the earth must pass through the 
point in question ; but the comet can only pass 
through the corresponding point in its path once 
in seven years. The earth moves in its orbit at 
the rate of about two millions of miles per day ; 
it consequently would remain within the limits 
of danger but a very brief period ; but unless 
that brief period precisely coincided with the 
moment in its seven years' circuit, at which the 
comet should pass through the corresponding 
point, the effect which we have now alluded to 
could not take place. * 

* The question of the near approach of comets 
to the earth, and of the effects of such an occur- 
rence, has been very fully and satisfactorily in- 
vestigated by Du Sejour.t He shows that of all 
the comets whose paths had been then ascer- 
tained, none could pass nearer to the earth than 
about twice the moon's distance ; and that none 
ever did pass nearer to the earth than nine times 
the moon's distance. This occurred with the 
comet of 1770, already mentioned as having 
been changed in its course twice by the action 
of Jupiter. The least unreasonable ground of 
apprehension from the proximity of a comet, 
would be the possible production of a tide in 
the ocean, which would so disturb its equilibri- 
um as to submerge considerable tracts of land. 
But to accomplish this, or, indeed, to raise a tide 
at all, it is necessary (even admitting that the 
disturbing body can exert sufficient attraction) 
that the angular motion of the attracting body, 
with respect to the earth, should not exceed a 

* In the year 1832, Biela's comet arrived at the point of 
its orbit nearest the earth on the 30th of October, and en- 
veloped within its limits a part of the earth's path ; but the 
earth did not arrive at the corresponding point of its orbit 
until the 30th of November; and since the earth moves at 
the rate of two millions of miles per day. its distance from 
the comet on the 30th of October must have been sixty 
millions of miles. 

t Traite analyuque <ics mouvemens apparens ties corps I 
celestes. Pans, 1785-.1739. 



certain rate. The moon only produces the tides 
because its angular motion is considerably under 
this limit. Du Sejour has proved that a comet 
could not, by possibility, remain more than two 
hours and a half so near the earth as a fourth 
part of the moon's distance. And it could not 
remain even so long unless it passed the earth 
under a very peculiar and improbable combina- 
tion of circumstances. For example, if its orbit 
were nearly perpendicular to that of the earth, 
it could not remain more than half an hour in 
such a position. Under such circumstances, the 
production of a tide would be impossible. He 
shows that eleven hours at least would be neces- 
sary to enable a comet to produce an effect on 
the waters of the earth, from which the injuri- 
ous consequences so much dreaded could follow. 
The conclusion to which he arrives is, therefore, 
that " although in strict geometrical rigor, it is 
not physically impossible that a comet should en 
counter the earth, yet the moral possibility of 
such an event is absolutely nothing." 

* The determination of the number of comets 
connected with our system is a question, which, 
although not admitting of a demonstrative solu 
tion, may be solved upon grounds of a high de 
gree of probability ; and it is one of so much in- 
terest, that we are induced here to extend the 
limits we had intended for this article, in order 
to lay before our readers the views of M. Arago 
and others on this j^oint. 

* The total number of distinct comets, whose 
paths during the visible parts of their course, 
had been ascertained up to the year 1832, was 
one hundred and thirty-seven. In order to dis- 
cover whether bodies of this nature prevail more 
in any particular regions of space than in others 
— whether, like the planets, they crowd into a 
particular plane, or are distributed through the 
universe without any preference of any one re- 
gion to any other — it was necessary to examine 
and compare the paths of these hundred and 
thirty-seven bodies. After a close examination 
of the planes of their orbits with respect to that 
of the earth, it appears, that the numbers in- 
clined at various angles, from to 90°, is pretty 
nearly the same. Thus, at angles between 80° 
and 90° there are fifteen comets; while at angles 
between 10° and 20° there are thirteen ; and be 
tween 30° and 40° there are seventeen. Again, 
the points, where they pass through the plane of 
the earth's orbit, are found to be uniformly dis- 
tributed in every direction around the sun. The 
points where they pass nearest to the sun are 
likewise distributed uniformly round that body. 
Their least distances from the sun also vary in 
such a manner as leads to the supposition of their 
uniform distribution through space. Thus, if we 
suppose a globe of which the sun is the centre 
to pass through the orbit of Mercury, so as to 
inclose the space round the sun, extending a 
distance on every side equal to the distance of 
Mercury, thirty of the ascertained comets, when 
at their least distance from the sun, pass within 
that globe. Between that globe and a similar 
one through the orbit, of Venus, forty-four com- 
ets pass under like circumstances. Between the 
latter globe and a like one through the orbit of 
the earth, thirty-four pass: between the globe 
through the orbit of the earth and one through 
ihs orbit of Mart), twenty-three pass; and be- 



70 



Arago and Lar drier's Astronomy. 



tween the latter and a globe through the orbit 
of Jupiter, six pass. No comet has ever been 
visible beyond the orbit of Jupiter. It must be 
here observed, that beyond the orbit of Mars it 
is extremely difficult to discern comets ; and 
this may account for the comparatively small 
number of ascertained comets which do not 
come nearer to the sun than that limit. A com- 
parison of the above numbers with the spaces 
included between these successive imaginary 
globes, and with the relative facility or difficulty 
of discerning comets in the different situations 
thus assigned, leads to a demonstration, that, so 
far as these hundred and thirty-seven observed 
comets can be considered as an indication of the 
general distribution of comets through space, 
that distribution ought to be regarded as uniform ; 
that is, an equal number of comets have their 
least distances included in equal portions of 
space. 

* Adopting, then, this conclusion, M. Arago 
reasons in the following manner : The number 
of ascertained comets, which at their least dis- 
tances pass within the orbit of Mercury, is thirty. 
Now, our most remote planet, Herschel, is forty- 
nine times more distant from the sun than Mer- 
cury ; consequently a globe, of which the sun 
is the centre, and w r hose surface would pass 
through the orbit of Herschel, would include a 
space greater than a similar globe through the 
orbit of Mercury in the proportion of the cube 
of forty-nine to one. Assuming the uniform dis- 
tribution of comets, it will follow, that for every 
comet included in a globe through the orbit of 
Mercury when at its least distance, there will 
be a hundred and seventeen thousand, six hun- 
dred, and forty-nine comets, similarly included, 
within the globe through the orbit of Herschel. 
But as there are thirty ascertained to be within 
the former globe, there will therefore be three 
millions, five hundred and twenty-nine thousand, 
four hundred and seventy within the orbit of 
Herschel. 

* Thus it appears that, supposing no comet 
ranging within the limits of Mercury has escaped 
observation, that portion of space inclosed with- 
in the globe through Herschel, must be swept 
by at least three millions and a half of comets. 
But there can be no doubt that much more than 
thirty comets pass within the globe through 
Mercury ; for it would be contrary to all proba- 
bility to assume that, notwithstanding the many 
causes obstructing the discovery of comets, and 
the short time during which we have possessed 
instruments adequate to such an inquiry, we 
should have discovered all the comets ranging 
within that limit. It is, therefore, more proba- 
ble that seven millions of comets are inclosed 
within the known limits of the system, than the 
lesser number ! Such is the astounding conclu- 
sion to which M. Arago's reasoning leads. 

* The light of comets is an effect of which 
astronomers have hitherto given no satisfactory 
account. If any of these bodies had been ob- 
served to have exhibited phases like those of 
the moon and the inferior planets, the fact of 
their being opaque bodies, illuminated by the 
sun, would be at once established. But the ex- 
istence of such phases must necessarily depend 
upon the comet itself being a solid mass. A 
mere mass of cloud or vapor, though not self lu- J 



minous, but rendered visible by borrowed light, 
would still exhibit no effect of this kind : its 
imperfect opacity would allow the solar light to 
affect its constituent parts throughout its entire 
depth — so that, like a thin fleecy cloud, it would 
appear not superficially illuminated, but receiv- 
ing and reflecting light through all its dimen- 
sions. With respect to comets, therefore, the 
doubt which has existed is, whethei*the light 
which proceeds from them, and by which they 
become visible, is a light of their own, or is the 
light of the suu shining upon them, and reflect- 
ed to our eyes like light from a cloud. For a 
long period this question was sought to be deter- 
mined by the discovery of phases. M. Arago 
then proceeded to apply to the question a very 
elegant mode of investigation, depending on a 
property* by which reflected light may be dis- 
tinguished from direct light, and the existence 
of which property there are sufficient optical 
means of delecting. He has, however, within 
the last year, furnished us, as we conceive, much 
more simple and satisfactory means of putting 
the question finally at rest ; if, indeed, it be not 
already decided. 

* It is an established property of self-shining 
bodies, that at all distances from the eye they 
have the same apparent splendor. Thus the 
sun, as seen from the planet Herschel, seems as 
bright as when seen from the earth. It is true 
that he is much smaller, but still equally bright. 
The smallest brilliant may be as bright as the 
largest diamond. We must not here be under- 
stood to imply that he affords the same light ; 
that is quite another effect. What is intended 
to be conveyed, will perhaps be best understood 
by considering the effect of viewing the sun 
through a pin hole made in a card. The card 
being placed at a small distance from the eye, it 
is evident that the eye will view only a small 
portion of the sun's disk, limited by the magni- 
tude of the pin hole ; but that portion, do far as 
it goes, will be as bright as it would be were the 
card removed. Now, the effect here produced, 
by limiting the portion of the sun's disk which 
the eye is permitted to see, is precisely the same 
as if the eye were carried to so great a distance 
from the sun, that its apparent magnitude would 
be reduced to equality with that portion of its 
disk which is seen through the hole in the 
card.t 

* Now, applying this principle to the question 
of cometary light, it will follow that, if a comet 
shines by light of its own, and not by light re- 
ceived from the sun, it will, like all other self- 
luminous bodies, have the same apparent bright- 
ness at all distances. It will therefore cease to 
be visible, not from want of sufficient apparent 
brightness, but from want of sufficient visual 
magnitude. Now, it may be shown that the 
limit of visual magnitude which would cause 
the disappearance of a self-luminous body is so 
extreme, that it would be totally inapplicable to 
this case. By varying the magnitude of the ob- 
ject-glass of a telescope (which may be easily 
done), with which such a body is viewed, in 
proportion to the magnifying power of the eye- 



* Polarization, 
f This property is demonstrable by mathematical re - 



Arago and Lardner's Astronomy. 



71 



glass, it is always possible to make the image of 
the same apparent brightness ; that is, supposing 
the object itself to maintain a uniform splendor. 
Consequently, if a body, submitted to this spe- 
cies of observation, cease to be visible even by a 
telescope, it will follow, that it must disappear 
either by a very extreme diminution of visual 
magnitude, or by the loss of its own intrinsic 
splendor. W*ow, to apply this test to the ques- 
tion of comets. Let us ask in what manner they 
disappear ? Is their disappearance the conse- 
quence of an excessive diminution of visual 
magnitude ? or is it to be attributed to the di- 
minished quantity of light which they transmit? 
Every astronomer will immediately a'eply that 
the latter only can cause the disappearance. 
The greater number of comets, including the 
most brilliant and remarkable one, of 1680 more 
especially, have obviously disappeared by the 
gradual enfeeblement of their light. They 
were, as it were, extinguished. At the very 
time they ceased to be visible, they possessed 
considerable visual magnitude. But such a 
mode of disappearance is incompatible with the 
character of a self-luminous body, unless we 
suppose that, from some physical cause, it grad- 
ually loses its luminosity. 

* But,in answer to this is adduced the observed 
fact, ttiat the dimensions of comets are enlarged 
as they recede from the sun ; that the luminous 
matter, thus existing in a less condensed state, 
will shine with a proportionally enfeebled splen- 
dor : and that at length, by the dilation of the body, 
the light becomes so dilute, that it is incapable 
of affecting the retina so as to produce sensation. 

* In answer to this objection, M. Arago has 
submitted to examination the rate at which 
comets increase their dimensions as they recede 
from the sun, according to Valez ; and calculates 
the corresponding diminution of intrinsic splen- 
dor which would arise from such a cause. The 
question then is, whether, by such a diminution 
of splendor, the brightest comets would be in- 
visible beyond the orbit of Jupiter? This question 
he proposes to decide by the following experi- 
mental test, to be applied to some future comet. 

* Let a telescope be selected having a large 
opening and low magnifying power, by the aid 
of which the comet may be observed in every 
part of its visible course. Let the body be ob- 
served with this instrument, at some determinate 
distance from the sun, such as, for example, the 
distance of Venus. M. Arago shows how, by 
applying different magnifying powers to the tel- 
escope under these circumstances, the image of 
the comRt may be made to assume different de- 
grees of brightness. He shows, also, how the 
magnifying power may be regulated, so as to ex- 
hibit the image of the comet with just that de- 
gree of brightness with which it would appear 
at any given increased distance to the lowest 
magnifying power; on the supposition of its be- 
ing a self-shining body, losing brightness by rea- 
son of the enlargement of its dimensions. In 
this way, he shows that the actual brightness 
which the comet ought to have at any given dis- 
tance from the sun, when looked at with any 
given magnifying power, may be predicted. He 
proposes, then, that, this observation being pre- 
viously made, the comet should be observed sub- 
sequently at the proposed distances. If it ap- 



pear with that degree of brightness which if. 
ought to have in correspondence with such pre 
vious observations, then there will be a presump- 
tion that it shines v,ith its own light. But if, as 
is probable, and perhaps nearly certain, the 
splendor of the comet at increased distances will 
be greatly less than it ought to be, and that it 
will be wholly invisible at distances at which it 
ought to be seen, then there will be conclusive 
proof that it is a body not self-luminous, but one 
which derives its light from the sun ; and that 
its disappearance, when removed to any consid- 
erable distance from that luminary, arises from 
the extreme faintness of the light which its at- 
tenuated matter reflects. 

* It will, of course, be perceived, that the en- 
largement of the volume of the comet will pro- 
duce a diluting effect upon its reflected light, as 
much as it would if it shone with direct light ; 
and this furnishes an additional reason for its ra- 
pid disappearance as it recedes from the sun. 

* It will doubtless excite surprise, that the di- 
mensions of a comet should be enlarged as it re- 
cedes from the source of heat. It has been often 
observed in astronomical inquiries, that the 
effects, which at first view seem most improba- 
ble, are nevertheless those which frequently 
prove to be true ; and so it is in this case. It 
was long believed that comets enlarged as they 
approached the sun; and this supposed effect 
was naturally and probably ascribed to the heat 
of the sun expanding their dimensions. But 
more recent and exact observations have shown 
the very reverse to be the fact. Comets increase 
their volume as they recede from the sun; and 
this is a law to which there appears to be no 
well-ascertained exception. This singular and 
unexpected phenomenon has been attempted to 
be accounted for in several ways. Valz ascribed 
it to the pressure of the solar atmosphere acting 
upon the comet; that atmosphere, being more 
dense near the sun, compressed the comet and 
diminished its dimensions ; and, at a greater dis- 
tance, being relieved from this coercion, the body 
swelled to its natural bulk. A very ingenious 
train of reasoning was produced in support of 
this theory. The density of the solar atmosphere 
and the elasticity of the comet being assumed to 
be such as they might naturally be supposed, the 
variations of the comet's bulk were deduced by 
strict reasoning, and showed a surprising coinci- 
dence with the observed change in the dimen- 
sions. But this theory is tainted by a fatal error. 
It proceeds upon the supposition that the comet, 
in the one hand, is formed of an elastic gas or 
vapor ; and, on the other, that it is impervious to 
the solar atmosphere through which it moves. 
To establish the theory, it would be necessary to 
to suppose that the elastic fluid composing the 
comet should be surrounded by a ?iappe or en- 
velop as elastic as the fluid composing thecomet. 
and yet wholly impenetrable by the solar atmo- 
sphere. 

* Several solutions of this phenomenon have 
been proposed by Sir John llerschel:* one is, 
that the comet consists of a cloud of particles, 
which either have no mutual cohesion, or none 
capable of resisting their solar gravitation; that, 
therefore, these particles move round the sun as 

* Memoirs Royal Astron. Soc. Vol. VI. p. 104. 



72 



Arago and Lar drier' s Astronomy. 



separate and independent planets, each describing 
an ellipsis or parabola, as the case may be. If 
this be admitted, it is demonstrable on geometri- 
cal principles, and, indeed, it follows as a neces- 
sary consequence of the principle of gravitation, 
that the particles thus independently moving, 
must converge as they approach the sun, so as to 
occupy a more limited space, and to become con- 
densed ; and that on receding from the sun, they 
will again diverge and occupy increased dimen- 
sions. 

* Herschel insists upon this the more, because 
he conceives it has the character of a vera causa. 
The fact is, the hypothetical part of it consists, 
not in the assumed effect of the gravitation of the 
particles of the comet, but in the assumption that 
the mutual cohesion or mutual gravitation of 
these particles is a quantity evanescent in com- 
parison with their separate gravitation toward 
the suu. This can scarcely be ranked as anything 
but a supposition assumed to account for the phe- 
nomena. 

* Another theory proposed by Sir John Hers- 
chel, which indeed is not altogether incompati- 
ble with the simultaneous operation of the former 
cause, is, that the nebulous portion of the comet, 
or that portion which reflects the sun's rays, is of 
the nature of a fog, or a collection of discrete 
particles of a vaporizable fluid floating in a trans- 
parent medium ; — similar, for example, to the 
cloud of vapor which appears at some distance 
from the spout of a boiling kettle. Now, since 
these molecules, during the comet's approach to \ 
the sun, absorb its rays and become heated, a por- 
tion of them will be constantly passing from the 
liquid to the gaseous or invisible state. As this I 
chang3 must commence from without, and must j 
be propagated inwards, the effect will be a dimi- 
nution of the comet's visible bulk. On the other 
hand, as it retreats from the sun, it will lose by 
radiation the heat thus acquired ; which, in con- 
formity with the general analogy of radiant heat, 
will escape chiefly from the unevaporated or ne- 
bulous mass within. The dimensions of this will, 
therefore, begin, and continue to increase by the 
precipitation immediately above it of fresh nebu- 
la ; just as we see fogs in cold and still nights 
forming on the surface of the earth, and gradual- 
ly extending upwards as the heat near the sur- 
face is dissipated. The comet would thus ap- 
pear to enlarge rapidly in its visible dimensions, 
at the moment that its real volume is in fact slow- 
ly shrinking by the general abstraction of heat 
from the mass. 

* " This process," says Sir John Herschel, 
' might go on in the entire absence of any solid 
or fluid nucleus ; but supposing such a nucleus 
to exist, and to have acquired a considerable in- 
crease of temperature in the vicinity of the sun, 
evaporation from its surface would afford a con- 
stant and copious supply of vapor, which, rising 
into its atmosphere, and condensing it at its ex- 
terior parts, would tend yet more to dilate the 
visible limits of the nebula. Some such process 
would naturally enough account for the appear- 
ances which have been noticed in the head of 
certain comets, where a stratum void of nebula 
has been observed, interposed, as it were, be- 
tween the denser portion of the head, or nucleus, 
and the coma. It is analogous to the meteoro- 
logical phenomenon of a definite vapor plane, so 



commonly observed ; and in certain cases, may 
admit of two or more alternations of nebula and 
clear atmosphere." 

* Sir John offers a third supposition to account 
for the effects, by attributing them to the ethereal 
medium surrounding the sun. 

* " Fourier," says he, " has rendered it not im- 
probable, that the region in which the earth cir- 
culates has a temperature of its ownjjreatly su- 
perior to what may be presumed to be the abso- 
lute zero, and even to some artificial degrees of 
cold. I have shown, I think, satisfactorily, that 
if this be the case, such temperature cannot be 
due simply to the radiation of the stars, but must 
arise from some other cause, such as the contact 
of an ether, possessing itself a determinate tem- 
perature, and tending, like all known fluids, to 
communicate this temperature to bodies im- 
mersed in it. Now, if we suppose the tempe- 
rature of the ether to increase as we approach 
the sun, which seems a natural, and indeed a 
necessary consequence, of regaining it as endued 
with the ordinary relations of fluids to heat, we 
are furnished with an obvious explanation of 
the phenomenon in question. A body of such 
extreme tenuity as a comet, may be presumed 
to take very readily the temperature of the 
ether in which it is plunged ; arid the vicissitude 
of warmth and cold thus experienced, may al- 
ternately convert into transparent vapor, and re- 
precipitate the nebulous substance, just as we 
see an increase of atmospheric temperature dis- 
sipate the fog, not by abstracting or annihilating 
its aqueous particles, but by causing them to 
assume the elastic and transparent state which 
they lose, and again appear in fog when, the tem- 
perature sinks."* 

PHYSICAL CONSTITUTION OF COMETS. 

This branch of cometary astronomy is not 
much developed : we shall, however, make 
known the state of the science as to the ckeve- 
lure, the nucleus, and the tail. 

A great number of those comets which have 
hitherto been observed, have no tail ; several 
present no apparent nucleus ; but all appear en- 
veloped in that nebulosity to which has been 
assigned the name of chevelure. 

The matter which constitutes the nebulosity 
is so rare, so transparent, that it allows the fee- 
blest light to traverse it, and the smallest stars 
can be perceived through it. 

In the comets that have a nucleus, the parts 
of the chevelure near the nucleus are usually 
rare, transparent, and of little brilliancy ; but 
at a certain distance from the nucleus the ne- 
bulosity suddenly brightens, so as to form, as it 
were, a luminous ring round the comet. Two 
of these concentric rings have sometimes been 
seen separated by obscure intervals. Of course, 
it will be understood that what in projection 
appears a circular ring, must in reality be a 
spherical envelope. 

When the comet has a tail, the ring is in the 
form of a semicircle, the convexity of which is 
turned toward the sun, and from its extremities 
issue the extreme rays of the tail, 

The ring of the comet of 1811 was 28,000 
miles thick ; it was 33,000 miles distant from 

* The preceding part of this lecture is by Dr. Lardne?* 
the remainder from M. Arago. 



Arago and Lardjier's Astronomy. 



73 



the nucleus. The comets of 1807 and 1799 had 
also rings of 33,000 and 22,000 miles in thick- 

3SS. 

We have said there exist comets that have no 
apparent nucleus ; these are no doubt only 
globes of gaseous matters ; but some there are 
that exhibit nuclei somewhat similar to planets 
both in form and lustre. These nuclei are usual- 
ly very st*f I ; sometimes, however, they are 
of large dimensions ; several have been measur- 
ed varyiug from 11 to 1089 leagues in diameter. 
Some astronomers have sought to prove, upon 
the strength of different observations, that the 
nuclei of comets are always transparent ; or, in 
other words, that comets are mere collections of 
gaseous matters. But, besides that the observa- 
tions cited in support of this opinion prove noth- 
ing in favor of the absolute terms in which it is 
expressed, they are in direct contradiction with 
other observations not less deserving of confi- 
dence ; and from the discussion of these differ- 
ent observations, it seems to result that there are 
comets that have no nucleus, comets whose nu- 
clei are perhaps transparent, and, lastly, very 
brililant comets, the nuclei of which are proba- 
bly solid and opaque. 

We have very little accurate knowledge re- 
specting the tails of comets. 

These luminous trains are usually directed 
from the sun, but sometimes they deviate more 
or less from this position. It has been found 
that the tail generally leans toward the region 
the comet has just quitted. This is, perhaps, an 
effect of the resistance of the ether, a resistance 
which acts more strongly on the gaseous tail 
than on the nucleus. This hypothesis will ac- 
quire more probability, if we remark that the 
deviation is the greater the more the distance 
from the head. Upon this principle the curve 
sometimes affected by the tail would seem to 
be the result of these differences of deviation, 
and this explanation is sufficiently in keeping 
with the circumstance that the convexity of the 
curve is always turned toward the region to 
which the comet is moving. The difference in 
density and brilliancy between the nebulous 
matter and the tail, the form of the latter more 
distinctly terminated on the side toward which 
the motion is directed, — all these circumstances, 
and some others which observations have made 
known, are equally and naturally explicable by 
the hypothesis 

The comet's tail enlarges and recedes from 
the head, and the middle region is usually occu- 
pied by a dark band, which has been taken for 
the shadow of the body of the comet. But this 
explanation is not suitable to every case, what- 
ever be the situation of the tail relatively to the 
sun. The phenomenon may be more satisfac- 
torily explained by supposing that the tail is a 
hollow cone, the side of which is of a certain 
thickness. It is easy to conceive that if this be 
the case, the eye must, on looking at the edges of 
the cone, encounter a greater number of nebu- 
lous particles than on looking at the central re- 
gion ; now, as the intensity of the light is in 
proportion to the number of these particles, the 
existence of the luminous bands and of the com- 
paratively obscure interval is readily intelligible. 
Comets are sometimes seen with several tails. 
That of 1744, for instance, on the 7th and 8th of 



March, had six tails, perfectly distinct, and sepa- 
rated from each other by obscure spaces. 

The tails of comets are sometimes of enormous 
dimensions. Some have been seen, as, for in- 
stance, those of 1680, of 1769, and of 1618, that 
reached the zenith while their tails still touched 
the horizon. That of the comet of 1680 has been, 
estimated at more than one hundred and four- 
teen millions of miles. 

But what are the tails of comets ? How are 
they formed? What are the causes that modify 
their shape in so many ways ? W T hat are the 
causes of the chevelure, and of the concentric 
envelopes of which it is sometimes formed? 
These questions have not yet been solved in a 
satisfactory manner. 

At first sight it would seem that the nebulosi- 
ty of comets can be nothing else but a mass of 
vapor disengaged from the nucleus by the action 
of the sun : but this very simple explanation 
does not account for the formation of the con- 
centric envelopes, for the variable position of 
the chevelure with respect to the sun, for the 
augmentation and diminution of its volume, &c. 
With respect to this latter point, however, we 
possess some information. Hevelius advanced 
the assertion, that the nebulosity augments in 
diameter in proportion as it recedes from the 
sun; and Newton attempted to explain this by 
saying, that the tails of comets, being formed at 
the expense of the chevelure, the latter must di- 
minish in volume as it approaches the sun, and 
again augment after passing the perihelion, when 
the tail restores to it the matter it had borrowed 
from it. It seemed difficult, however, to admit 
that a gaseous mass should become dilated in 
proportion as it receded from the sun to pass in- 
to colder regions ; and the important remark of 
Hevelius obtained little favor, till the comet of 
short period came, and most strikingly confirm- 
ed it. 

Kepler thought the formation of the tail of 
comets was owing to the impulse of the solar 
rays detaching and dispersing the lighter parti- 
cles of the nebulosity. But before this doctrine 
can be admitted, it must be proved that the so- 
lar rays are endowed with any impulsive force, 
Now the most delicate experiments have not de- 
tected any in them ; and, if this impulsive force 
were admitted, it might still be asked, why the 
tail is not always situated opposite to the sun ? 
why there are sometimes several at such large 
angles with each other ? why they are formed 
and vanish in so short a space of time ? why some 
have a very rapid rotary motion ? lastly, why 
there are comets the nebulosity of which appears 
very delicate, very light, and which yet have 
no tail ? 

A host of other theories have been propound- 
ed on this subject, more or less ingenious, but 
they have all broken down when tested by the 
phenomena. 

Are comets luminous in themselves, or do 
they, like the planets, shine only by a borrowed 
light ? This important question has not yet re- 
ceived a complete solution, but there exist 
several meaus of solving it. Should we ever 
detect the phenomena of phases in the comets, 
the question would be set at rest. For want of 
phases, the phenomena of polarization may lead 
to the same result. Lastly, the following is a 



74 



Arago and Lardner's Astronomy, 



third method, the application of which, when- 
ever it can be made, will probably remove every 
doubt. 

Suppose a self-luminous point without sensi- 
ble dimensions, radiating particles of light all 
round it through space. If at the distance of 
one yard, for instance, we receive these lumi- 
nous particles on the surface of a sphere of one 
yard radius, they will be equally divided over it. 
If they be received at the distance of two, three 
— one hundred yards, the spheres being two, 
three — one hundred yards in radius, the lumi- 
nous molecules will spread uniformly over them, 
but will diverge from each other in proportion to 
the enlargement of the surfaces of the spheres. 
Now, geometry teaches us that the surfaces of 
spheres increase proportionally to the squares of 
their radii ; the divergence of the rays of light will, 
therefore, be likewise proportional to the squares 
of the radii, or, in other words, to the squares 
of the distances at which the luminous molecu- 
les are received; and if the intensity of the light 
which illuminates an object is proportional to the 
number of luminous rays incident upon it, we ar- 
rive at this law, that the luminous intensity of a 
point diminishes inversely as the squares of the 
distances. 

Hitherto we have supposed the case of a lu- 
minous point without sensible dimensions ; let 
us now give it some extension. 

It is evident that each point of the illumina- 
ting surface will project, like the isolated point 
we have just spoken of, a light which will di- 
minish in the inverse proportion of the squares 
of the distances. Only, the number of points 
being augmented, the total quantity of light is- 
sued will be greater; whence it follows, that at 
equal distances the intensity of light is propor- 
tionate to the number of radiant points. 

We are arrived, then, at this two-fold conclu- 
sion, that the illuminating power of a surface is, 
on the one hand, pi*oportional to its extent, and 
on the other, is in the inverse ratio of the 
squares of the distances. 

The consequence of this law is, that the inten- 
sity of a luminous surface must appear the same, 
at whatever distance the surface be transported, 
provided it always subtends a sensible angle. 

That this consequence may not at first view 
appear contradictory to the law from which we 
have deduced it, we must remark, that the sec- 
ond case concerns the intensity of a luminous 
surface, and the first its illuminating power. 

When we wish to compare, not the illumina- 
ting power, but the luminous intensity of the 
two surfaces, we must take an equal portion of 
each of them, and see which is the more bril- 
liant. This being laid down, I say that, two 
luminous surfaces being given, if through open- 
ings of equal dimensions we expose equal por- 
tions of them to the eye, and if these portions 
appear to possess the same intensity, they will 
do so as well when one of the surfaces is trans- 
ferred to a greater distance, provided always, 
that the opening through which a part of the 
surface is seen appear always filled. 

For if, on the one hand, each luminous point 
sends to the eye a number of rays in the inverse 
ratio of the square of the distance, on the other, 
the- number of luminous points which the eye 
discovers through the opening, increases in the 



same direct proportion. The intensity of the 
visible portion of the luminous surface, will, 
therefore, have undergone no change. The sun, 
for instance, as seen from Uranus, appears a cir 
cle of 100 seconds. Well then, let us cut out 
upon the sun's disk, by means of a screen with a 
hole in it, a circular surface of 100 seconds, and 
we shall have the sun of Uranus both in size and 
lustre. fe 

Let us now see to what use these principles 
may be turned for solving the question we have 
in view, namely, whether the comets are or are 
not self-luminous. 

The question resolves itself into this : In what 
manner does a comet cease to be visible ? If its 
disappearance is the result of an excessive dim- 
inution of its dimensions, and not of a weaken- 
ing of its light, the star is self-luminous ; but if, 
the comet being still of large dimensions, its 
light gradually fades, and finally becomes ex- 
tinct, that light no doubt was borrowed. 

The observations hitherto made, seem to prove 
that this cause of the disappearance is the true 
one, and ; consequently, that the comets only re- 
flect a borrowed light. 

Nevertheless, this consequence may possibly 
not be rigorously exact. It is now ascertained, 
as already stated, that the nebulosity of comets 
increases as they recede from the sun May it not 
be that this progressive dilatation causes a grad- 
ual weakening of the light ? Henceforth then it 
will be necessary to investigate the cause of the 
dilatation, and to show that it is insufficient to 
explain the disappearance of comets. This com- 
plication of the problem cannot present any great 
difficulties. 

There are some questions connected with 
cometary astronomy which we shall examine iii 
succession. 

Have comets a sensible influence on the course 
of the seasons ? 

This question has been decided in the affirma* 
tive by popular prejudice, fortified by exam- 
ples; among which the fine comet of 1811, and 
the abundant harvest that followed it, are not 
forgotten. A few words will suffice to confute 
this error. Let us first speak of facts ; theoreti- 
cal considerations will follow after. 

The inquiry has been made, on examining the 
thermometrical observations which are taken 
several times daily in observatories, whether the 
mean temperatures of years distinguished by 
comets, are higher than those of other years ; no 
sensible difference has been discovered. 

The result of these observations is in accord- 
ance with theory. By what mode of action, in- 
deed, could comets modify our temperature ? 
They can only act at distance upon the earth by 
attraction, by the luminous and calorific rays they 
emit, and by the gaseous matter of their tails, 
which might possibly expand into our atmo- 
sphere. 

The attractive force of the comets might, cer- 
tainly, if it was strong enough, occasion tides 
similar to those caused by the moon ; but we 
cannot see how fin elevation of temperature 
should arise from it. 

Neither could the calorific or luminous rays, 
which comets emit or reflect, produce this effect, 
for they are of much less intensity than those 
that reach us from the moon, and which, con- 



Arago and Lardner's Astronomy. 



75 



centrated in the foci of the largest lenses, pro- 
duce no sensible effect. 

Lastly, the introduction of a part of the tail of 
a comet into the atmosphere cannot be assigned 
as the cause of the elevation of temperature at- 
tributed to these bodies, since the tail of the 
comet of 1811, for instance, which was forty-one 
millions of leagues long, never reached the earth, 
nor came wi0m several millions of leagues of it. 

Is it possible thai a comet should come in collis- 
ion with the earth, or any other planet 1 

Comets move in ail directions in very elonga- 
ted ellipses, which traverse our solar system and 
crosss the orbits of the planets. It is not, there- 
fore, out of the range of possibility that they 
should come in contact with some eg these stars, 
and the shock of the earth by a comet is rigo- 
rously possible : at the same time it is extremely 
improbable. 

The evidence of this proposition will be com- 
plete, if we compare with the small volume of 
the earth and of comets the immensity of the 
space in which these globes move. The doc- 
trine of chances affords us the means of estima- 
ting numerically the probability of such a collis- 
ion, and shows that there is but one such chance 
in 281 millions: that is to say, that, on the ap- 
pearance of a new comet, the odds are 281 mil- 
lions to one that it will not strike against our 
globe. Hence we see how absurd it would be 
in man to concern himself with the apprehen- 
sion of such a danger, during the few years he 
has to pass upon the earth. 

Were this collision indeed to take place, its 
effects would be tremendous. Were the earth 
stricken, so that its motion in space should be 
destroyed, everything not adhering to its surface, 
as animals, water, &c, would set off from it 
with a velocity of seven leagues per second. If 
the shock only retarded the rotary movement, 
the seas would spring from their basins, the 
equator and the poles would be changed. But 
let us allow the author of the Mecanique Celeste 
himself to describe their terrible effects: " The 
axis and the rotary motion being changed, the 
seas would abandon their old positions, and rush 
violently toward the new equator ; a great part 
of the human and animal races drowned in this 
universal deluge, or destroyed by the violence 
of the shock given to the terrestrial globe ; en- 
tire species annihilated : all the courses of hu- 
man industry confounded ; — such would be the 
disasters ensuing from a collision with a comet. 
We now see why the ocean has covered the 
loftiest mountains, on which it has left the most 
incontestible traces of its presence ; we see why 
it is that animals and plants of southern climes 
have been able to exist in the north, where their 
remains and their footsteps are now discovera- 
ble; lastly, we can explain the novelty of the 
moral world, the monuments of which hardly 
ascend backward more than 5000 years. The 
human species, reduced to a small number, and 
to the most deplorable condition, solely occupied 
during a very long space of time with care of 
self-preservation, must necessarily have wholly 
lost the memory of arts and sciences ; and when 
at length the progress of civilization made it feel 
the nature of its wants, it had to begin every- 
thing anew, as if men had then for the first time 
been placed upon the earth." 



Has our globe ever been struck by a comet, as 
the author just quoted supposes ? 

Men of profound acquirements have asserted, 
that the axis on which our globe turns has not 
always been the same. This opinion they have 
supported by reasonings drawn from the fact, 
that the several degrees measured on each me- 
ridian between the pole and the equator, com- 
bined two and two, do not all give the same 
value for the flattening at the poles. In the dif- 
ference of these results they fancy they see a 
proof, that, at the time when the earth, still in 
the fluid state, assumed its sphericity, it did not 
turn on the same axis it does now. 

But it is easy to convince ourselves that the 
change in the axis cannot be the cause of the 
discrepancies between the value of degrees fur- 
nished by observation, and those which would 
result from a certain theory of flattening ; for this 
disagreement does not follow a regular and 
gradual course, but an irregular and capricious 
one. It is the result of local attractions, of geo- 
logical accidents, which we now know can exist 
as well in the plains as in the neighborhood of 
mountains. 

But let us pass on to other consideiations. 

If we give a rotary motion to a spherical and 
homogeneous body, freely suspended in space, 
its axis of rotation remains perpetually invaria- 
ble. If this body has quite a different form, its 
axis of rotation may change every moment ; and 
this multitude of axes, round which it executes 
only a part of its rotation, are called the instanta- 
neous axes of rotation. Lastly, geometry demon- 
strates that every body, whatever be its figure 
and its variations of density from region to re- 
gion, may turn in a constant and invariable man- 
ner round three axes perpendicular to each 
other, and passing through its centre of gravity. 
These are called the principal axes of rotation. 

This being premised, let us inquire whether 
the axis round which the earth turns is an in- 
stantaneous or a principal axis. In the former 
case the axis will change every instant, and the 
equator will undergo corresponding displace- 
ments. Terrestrial latitudes, which are no moi'e 
than the angular distances of the several places 
from the equator, will suffer the like changes. 
Now observations of latitude, which are made 
with extreme nicety, indicate no changes of this 
kind ; terrestrial latitudes are constant : the 
earth, therefore, turns on a principal axis. 

From this it is easy to deduce a proof that the 
earth has never sustained the shock of a comet ; 
for the effect of this would have been to substi- 
tute an instantaneous for the principal axis, and 
terrestrial latitudes would have been subjected to 
continual alterations, which observations do not 
discover. It is true, it is not mathematically im- 
possible that the effect of a shock should be to 
substitute a principal for an instantaneous axis, 
but this case is so improbable that it scarcely 
weakens the force of the demonstration. 

In what we have just said, we have proceed- 
ed on the supposition that the earth is a body 
entirely solid. But it may be that its interior is 
still liquid, as it is in the present clay generally 
supposed to be. Can we in this latter case de- 
duce, with the same certainty, from the constan- 
cy of terrestrial latitudes, a proof that the earth 
has never boon struck by a comet? 



76 



Arago ana Lardner's Astronomy. 



We think not: for, after the shock, the im- 
mediate effect of which would have been vio- 
lently to precipitate a part of the internal liquid 
mass toward the new equator, where it could 
not have lodged but by bursting through the 
solid crust of the globe, the continual displace- 
ment of the instantaneous axis inferring an in- 
cessant alteration in the shape of the fluid mass, 
it would not be impossible that the continual 
friction of the liquid against the solid shell, 
should bring about a gradual diminution in the 
length of the curve described by the extremities 
of the instantaneous axis, and consequently, in 
the long ran, a motion of rotation round a princi- 
pal axis. 

Is it possible that the earth should pass through 
the tail of a comet, and what consequences would 
this produce for us ? 

Comets have in general very little density : 
they must, therefore, very feebly attract the 
matter forming these tails, since attraction op- 
erates in proportion to the mass. Now we can 
easily conceive that the earth, the mass of which 
is much more considerable than that of most 
comets, may attract to itself and draw into its 
atmosphere a part of the tails of those bodies, 
especially if we reflect that the extreme por- 
tions of the tails are sometimes at enormous dis- 
tances from the heads. 

As for the consequence of the introduction of 
a new gaseous element into our atmosphere, it 
would depend on the nature and the abundance 
of the matter thereof, and might occasion the to- 
tal or partial extinction of animal life. But sci- 
ence has not yet had an opportunity of recording 
an event of this nature; and the connection 
which many persons have sought to trace be- 
tween the appearance of comets and the revolu- 
tions of the moral and physical world, rests on 
no foundation. 

Were the dry fogs of 1783 and 1831 constitu- 
ted of matter detached from the tails of comets? 

The fog of 1783 lasted a month. It began ou 
the same day in places very remote from each 
other. It extended from the north of Africa to 
Sweden ; it occupied too a large part of North 
America, but it did not extend over the sea. It 
rose above the loftiest mountains. It did not ap- 
pear to be carried by the wind : and the most 
abundant rains, the strongest winds, were unable 
to dissipate it. It gave out a disagreeable odor, 
was very dry, did not at all affect the hygrome- 
ter, and possessed the property of phosphores- 
cence. 

Such are the facts : it has been sought to ex- 
plain them on the supposition that this fog was 
the tail of a comet. But if that were so, why 
was the head of the comet never seen, for the 
fo<* was not so dense as to hinder the stars from 
being visible at night 1 The objection is funda- 
mental, and saps the hypothesis at its base. 

This explanation is still less applicable to the 
fog of 1831, which so much resembled that of 
1783 ; for this fog, not having covered the whole 
surface of Europe, the invisibility of the comet 
would have been still more surprising. Besides., 
every point between the parallels should have 
been successively covered by reason of the 
earth's rotation, and yet the fog terminated at 
fifty leagues from the coasts. 

The origin of these extraordinary fogs may be 



more satisfactorily explained, as proceeding 
from the internal revolutions by which our glob© 
is often agitated. In 1783, the 6ame year as the 
fog appeared, Calabria was devastated by fright- 
ful earthquakes, that buried more than 40,000 of 
its inhabitants. Mount Hecla, in Iceland, made 
one of the greatest eruptions on record ; new 
volcanoes issued from the bosom of the sea, &c. 

Is it then so difficult to ad^t that gaseous 
matters, of an unknown nature, should have is- 
sued from the bowels of the earth, torn by these 
violent commotions, and may not this explana- 
tion be consistent with the remarkable circum- 
stance that the fog did not exist on the high seas? 
But we merely wish to point out one of those 
hypotheses on which it would be possible to ex- 
plain the formation of dry fogs, without having 
recourse to the immersion of the earth in the tail 
of a comet. 

There exists on the western coast of Africa, 
something similar to the phenomenon in ques- 
tion. It is a dry and periodical fog, conveyed by 
a wind called harmatan, which makes furniture 
crack, and warps the covers of books, dries up 
plants, and exercises over the human body a no 
less unfavorable influence. This fog, too, is con- 
fined to the land : its cause is unknown. 

Has the moon ever come in collision with a 
comet ? 

We have seen that the satellite turns on itself 
in precisely the time it takes to pei-form its rev- 
olution round the earth. The isochronism of, 
these motions is explained by supposing, that 
at the time when the moon, still fluid, was tend- 
ing to assume the form corresponding to its ro- 
tation, the attraction of our earth elongated it, 
and its great axis directed itself toward the cen- 
tre of the earth. 

Now if a comet had ever struck the moon, the 
shock would have disturbed the harmony exist- 
ing between the motions of rotation and revolu- 
tion, and consequently have caused the greater 
axis of the moon to be displayed from the line 
directed toward the centre of the earth. This 
great axis would then, like a pendulum, perform 
oscillatory motions round our earth; but nothing 
of the sort existing, we must therefore conclude 
that the moon has never been shocked by a 
comet. 

Has the moon formerly been a comet? 

The Arcadians, according to Lucian and Ovid, 
believed themselves more ancient than the 
moon. Their ancestors, they said, had inhabited 
the earth before the moon existed. This singu- 
lar tradition has suggested the question, whether 
the moon may not be an old comet, which, pass- 
ing near the earth, became its satellite. 

There is no impossibility in that; but the rea- 
sons given in support of this conjecture have not 
the slightest value. As the comet-moon, that it 
should become a satellite of the earth, must 
necessarily have had a short perihelion distance, 
speculators will have it that in the burnt appear- 
ance of its mountains, exist evidences of the 
enormous heat it must have endured in passing 
so near to the sun. This is a confusion of words. 
It is very true the appearances of ancient vol- 
canic derangements give to some points of the 
moon's surface a burnt aspect, but nothing ex- 
ists to indicate, in the present day, what tempe- 
rature it may formerly have sustained. 



Ara&o and Lardner's Astronomy. 



77 



Furthermore, the partisans of this opinion Will 
have some difficulty in explaining why the 
moon has no sensible atmosphere, whereas all 
the comets that have yet been seen, present 
themselves to us enveloped in a gaseous cover- 
ing. If the moon is an old comet, what has she 
done with her hair? 

is it possible that the earth should become the 
satellite of a c9met, and if so, what lot would in 
that case await us? 

That a comet should possess itself of the earth, 
and make it its satellite, it is enough to give it a 
mass sufficiently considerable, and to make it 
pass near us. It will, beyond doubt, take our 
globe away from the attraction of the sun, and 
carry it with it in its revolution round that body. 
But the great mass with which the supposed 
comet must be endowed, and the small distance 
at which it must pass from the earth, l'ender 
this event of little probability. 

However, as it is rigidly possible that the 
thing may happen, let us inquire what would 
under these circumstances be the fate of the 
earth's inhabitants. Would our globe undergo, 
as has often been asserted, extreme vicissitudes 
of temperature? Would it be by turns vitrified, 
evaporated, congealed ? Would it become un- 
inhabitable, and would all the animal and vege- 
table races on its surface be annihilated ? 

Let us suppose, in order to reply to these 
questions, that the earth becomes a satellite to 
a comet that approaches closely to the sun, and 
recedes to a great distance from it — the comet 
of 1680, for instance. 

This comet, supposing it to complete its revo- 
lution in 575 years, travels over an ellipsis, the 
major axis of which is 138 times greater than 
the mean distance of the earth from the sun. 
Its perihelion distance is extremely short. New- 
ton has calculated that at its perihelion of the 
8th of December, 1680, it must have sustained 
a heat 28,000 times greater than that of the earth 
in summer: he has estimated it at 2000 times 
that of red-hot iron. 

But this result cannot be admitted. To solve 
the problem that Newton proposed to himself, 
it would be necessary to know the state of the 
surface and of the atmosphere of the comet in 
1680: nay more, put the earth itself in the 
comet's place, and the question is not yet solved. 
Doubtless the earth will at first undergo a tem- 
perature 28,000 times greater than summer 
heat; but soon all the liquid masses that cover 
itbeiug converted into vapor, will produce thick 
layers of clouds, that will diminish the action of 
the sun in a proportion impossible to assign 
numerically. 

Would it be more easy to determine the tem- 
perature of our globe, when it shall have accom- 
panied the comet to its aphelion? If we con- 
sider only the relations of distance, the earth 
should then be 19,000 times less heated than it 
is in summer, that is to say, no longer receiving 
any appreciable heat from the sun, it should 
only possess that quantity not yet dissipated, 
which it should have imbibed at its perihelion, 
and if it had lost all this, it should be at the 
temperature of space or thereabouts, which can- 
not descend below fifty degrees, according to 
the ingenious computations of Fourier. 

Now experience proves that man can sustain 



degrees of cold of from forty-nine to fifty de- 
grees below zero of the centigrade thermome- 
ter, and a heat of 130 degrees, when he is 
placed in certain hygrometric conditions. There 
is nothing, therefore, to prove that in the hypo- 
thesis that the earth should become the satellite 
of a comet, the human race must necessarily 
perish from thermometric changes. 

These considerations as to the limits between 
which the temperatures of the celestial globes 
may oscillate , are fitted to render their inhabi- 
tability less problematical in the eyes of persons 
who feel a difficulty in conceiving the existence 
of beings formed upon a system of organization 
totally different from our own. 

Was the deluge occasioned by a comet ? 

It is impossible in the present day to doubt 
but that our globe has been frequently convulsed 
by frightful revolutions, and that the waters of 
the sea have repeatedly inundated and aban- 
doned the continents. To explain these tre- 
mendous cataclysms the aid of comets has been 
invoked. Let us examine these explanations. 

Whiston proposed one, which he had adapted 
to all the circumstances of the deluge described 
by Moses. He supposes, and there is nothing 
inadmissible in the supposition, that the comet 
of 1680 was in the neighborhood of the earth 
when the deluge happened. He makes the 
earth to be an old comet, to which he gives a 
solid nucleus, and two concentric orbs — the 
nearer to the centre formed of a weighty fluid, 
and the other of water; on this latter reposes 
the solid crust on which we walk. This being 
premised, he places the comet of 1680 at no 
more than 3000 or 4000 leagues from the earth. 
The comet, by reason of its great proximity, 
exercising a powerful attraction over the in- 
terior fluids, produced an immense tide that 
burst the solid crust, and precipitated the fluid 
mass upon the continents. This was the break- 
ing tip the fountains of the great deep.* 

As for the opening of the windows of heaven, 
as Whiston could not see this in ordinary rain, 
forty days and nights of which would have pro 
duced too inconsiderable results, he sought it in 
the atmosphere, and in the tail of his comet, 
which spread over our globe a sufficient quan- 
tity of aqueous vapors to supply the most violent 
rains. 

This theory, which long enjoyed great cele- 
brity, will not sustain any deep investigation. 

We shall not speak of the constitution attrib- 
uted by Whiston to the earth, and which is not 
admitted by modern geology. We shall confine 
ourselves to remarking, that his gratuitous sup- 
position of the mass and the proximity of the 
comet of 1680, is not sufficient to explain the 
phenomena. 

In fact, since the motion of the comet must 
have been extremely rapid, its attraction could 
not have been exerted for a sufficient length of 
time upon the several points, to cause the great 
tide of which we have spoken. 

Besides, this famous comet passed near the 
earth the 21st of November. 1680, and it is de- 
monstrable that at the epoch of the deluge it* 
distance was not less. For all that, it did not 
break up the fountains of the great deep, nor 

Genesis vii. 11 ; vii. 2. 



Aragc and Lardners Astronomy. 



open the windrows of heaven. Whiston's expla- 
nations are therefore inadmissible. 

Halley, who took a more general view of the 
question, endeavored to account for the pre- 
sence of marine productions far from the seas, 
and on the highest mountains, by the shock of a 
comet coming in contact with the earth. 

We have already examined the question, whe- 
ther such a shock has ever taken place. We 
shall here add that, supposing the affirmative of 
this question, we should vainly seek, in the ef- 
fects of such a collision, a satisfactory explana- 
tion of the phenomena. The stratification of the 
marine deposits, the extent and regularity of the 
strata, their positions, the perfect preservation 
in them of the most delicate and most fragile 
shells, all exclude the idea of a violent transfer 
of place, all prove that the deposits have been 
made where they are found. 

The explanation of these phenomena presents 
no difficulties, since science has been enriched 
by the brilliant ideas of M. Elie de Beaumont 
upon the formation of mountains by way of up- 
lifting of the land. 

Have the several points of our globe suddenly 
changed their latitude in consequence of the 
shock of a comet ? 

In every region of Europe are found fossil 
bones of the rhinoceros, the elephant, and other 
animals, which now could not live in our latitudes. 
We must therefore suppose, either that Europe 
has experienced a considerable cooling down, or 
that in some of the violent commotions our earth 
has undergone, these fossil remains have been 
swept along by currents carrying them from 
south to north. 

But these explanations are inapplicable to 
two circumstances discovered iu modern times, 
and which have greatly engaged the attention 
of the learned. On the banks of the Wilhoui 
in Siberia, in 1771, was found, at a few feet 
below the surface, a rhinoceros in a state of 
perfect preservation ; neither its flesh nor its 
skin was in the slightest degree damaged. At a 
later epoch, in 1799, there was found near the 
mouth of the Lena, on the shores of the Icy 
Sea, a great elephant inclosed in a mass of con- 
gealed mud, and so well preserved that dogs ate 
of its flesh. 

How are we to account for the presence of 
these two large animals at such a distance from 
the countries in which they lived ? Here the 
operation of currents cannot be thought of; for 
had not the animals been frozen immediately 
after death, they would have suffered putrefac- 
tion. They must, therefore, have lived in the 
places where they have been found. Thus, on 
the one hand, Siberia must formerly have pos- 
sessed an elevated temperature, since elephants 
and rhinoceri lived in it ; on the other, the ca- 
tastrophe in which these animals perished, must 
have suddenly rendered those regions icy. 

There remains but one step from these deduc- 
tions to the admission of the shock of the earth 
by a comet : for we know no other cause capa- 
ble of producing an abrupt alteration in the lati-j 
ludes of our globe. 

Is this explanation admissible 1 We think not. j 
In the first place, is it authenticated that the 
elephant of the Lena, and the rhinoceros of the I 
Wilhoui. could not have lived under the actual 1 



climate of Siberia? We may venture to doubt 
this ; for these animals, otherwise similar in size 
and form to those that now inhabit Africa and 
Asia, are distinguished from them by a circum- 
stance very deserving of note; they possessed a 
species of fur. The skin of the rhinoceros was 
beset with stiff hairs, from two to three tenths 
of an inch long, and that of the elephant was 
covered with black hairs and with a reddish 
wool; its neck was furnished with a long mane. 
These remarkable peculiarities impress us 
strongly with the notion that these animals were 
created to live in a northern region. 

Again, a celebrated traveller has recently es- 
tablished the fact, that the royal tiger, which 
belongs to the hottest countries, still lives in 
Asia in very elevated latitudes, that it advances 
in summer as far as to the western slope of the 
Altai mountains. Why might not the furred 
elephant have transported himself in summer as 
far as to Siberia? When arrived there, a very 
common accident, a snow-slip, for instance, was 
sufficient to bury him under frozen layers capa- 
ble of preserving him from all putrefaction: for 
in ihose latitudes, the earth, to a depth of from 
twelve to fifteen feet, remains eternally frozen. 
It is, therefore, by no means necessary, if we 
would account for the discoveries on the Lena 
and the Wilhoui, to have recourse to the suppo- 
sition of a comet's collision with the earth. 
Moreover, this hypothesis, the inadmissibility of 
which we have shown elsewhere, would in this 
case be of no avail. For if the partisans of this 
opinion will absolutely have it that Siberia was- 
formerly in the vicinity of the equator, it must 
necessarily be admitted that it was then covered 
by a fluid dilatation of more than five leagues 
thickness, produced by the rotary motion of the 
earth. Under these circumstances, where should 
we find footing for our rhinoceros and our ele- 
phant? 

M. Elie de Beaumont has ingeniously connect- 
ed the solution of the problem created by the 
discovery of the Siberian elephants with his the- 
ory of the formation of mountains. He supposes 
that the Tian Chan having risen in winter in a 
country the valleys of which abounded with ele- 
phants, and the mountains of which were cov- 
ered with snow ; the warm vapor issuing from 
the earth's bosom at the moment of the convul- 
sion partly melted this snow, and produced a, 
great current of air at the temperature of zero. 
This current laying hold of the carcasses of these 
animals itfound in its way, carried them with it in 
eight days, before decomposition could set in. 
into the latitudes of Siberia, where the frost im- 
mediately seized them. 

What is the cause of the depression of the soil 
exhibited by a great part of Asia I Is it the 
shock of a comet ? 

There is in Asia a vast region, 18.000 leagues 
square, occupied in a great measure by the Cas- 
pian Sea, and containing populous cities, which 
exhibits a depression of one hundred metres 
(three hundred and twenty-nine feet) below the 
level of the Black Sea and the Ocean. 

To explain this enormous sinking of a whole 
country, recourse has been had. as in so many 
other circumstances, to the supposed collision of 
the earth with a comet. 

This explanation, proposed by Halley, is now- 



Arago and Lardiier's 



Astronomy. 



79 



a days abandoned : the earth, we have seen, has j 
never come in collision with a comet, and the 
geographical phenomenon in question can be ex- 
plained without this supposition. 

It is an opinion, generally admitted in the 
present day, that mountains have been formed 
by the upheaving of their materials ; that they 
have issued from the bosom of the earth by 
breaking violently through its crust. Now the 
necessary consequence of such an uplifting, is 
the formation of a void in the surrounding soil, 
and the possibility of their subsequently fail- 
ing in. 

Let us cast our eyes on the map ; we shall see 
that Asia abounds more in upheaved masses 



than any other quarter of the globe, and that 
round the depressed region of which we have 
spoken tower a multitude of great chains: the 
Iran, the Himalayan, the Kuen Lun, the Tiau 
Chan, the Caucasian chain, the mountains of Ar- 
menia, those of Erzerum, &c. Why, therefore, 
should not the elevation of these great masses 
have caused a cox*responding sinking in the in- 
termediate soil? 

This explanation will appear still more plausi- 
ble, if we add, that, in the regions we are speak- 
ing of, the soil has not yet arrived at a state of 
complete stability, and that the bottom of the 
Caspian Sea, for instance, exhibits alternations 
of depression and elevation. 



LECTURE XII 

ECLIPSES. 



Eclipses, like comets, were formerly oDjects 
of popular terror, but every one now knows that 
these phenomena are consequences of the laws 
of nature, and they are predicted with as much 
accuracy as the return of day and night. 

ECLIPSES OF THE MOON. 

The earth being an opaque and round body, 
the sun can enlighten but a part of it at a time ; 
whence it follows, that it projects a shadow op- 
posite to that luminary. What is the form of 
this shadow ? What are its dimensions ? If the 
sun and the earth were of the same size, the 
shadow would be cylindrical, and of infinite ex- 
tent ; but as the earth is much smaller than the 



sun, the shadow it projects forms a cone, long" 
enough to reach the moon, but not sufficiently 
long to arrive at Mars: it has been calculated 
that this cone is 800,000 miles in length. On the 
sides of the cone are shadows less dense, formed 
by the interruption of a part only of the sun's 
rays, and the intensity of which diminishes in 
proportion as they recede from the conical shad- 
ow. This intermediate shade between pure 
shadow and light, is called the penumbra. To 
determine its limits, we may draw lines extend- 
ing from the edges of the sun and grazing the 
earth's surface. These prolonged lines form a 
truncated cone, which is that of the penumbj-a. 
Thus, let S be the sun, E the earth. The cone of 



Fig. 39 




snadow abf terminates in/, where the rays is- 
suing from the sun's edges meet after having 
grazed the earth's surface, and the truncated 
cone abed, is that which forms the penumbra. 

When the earth, then, becomes situated be- 
tween the sun and the moon, the latter must be 
covered with darkness, and there will be an 
eclipse of the moon. The eclipse will be total 
or partial, according as the moon plunges wholly 
or in part into the cone of a shadow. It will be 
central, if the centre of the moon coincides ex- 
actly with that of the terrestrial shadow. 

Were the plane in which the moon moves not 
inclined to the ecliptic, a lunar eclipse would 
take place at eveiy full moon: but as the orbit 
»t describes cuts the ecliptic according to the 
line of the nodes, it takes various positions rela- 
tively to this plane. If at its opposition, it is not 
in the nodes, it will skim the earth's shadow 



without penetrating it, and this is what most fre- 
quently occurs ; but if the line joining the centre 
of the earth, the sun, and the moon, is a straight 
line, or nearly so, as is the case when the moon 
is in or very near the nodes, there will be an 
eclipse. 

To express the extent of eclipses, the moon is 
supposed to be divided into twelve equal and pa- 
rallel zones, called digits. Thus, when a third, 
or one half of the disk is eclipse, d we say that the 
eclipse is of four or six digits. If the eclipse is to 
tal, and the diameter of the shadow is greater 
than that of the moon, we say that the eclipse is 
of more than twelve digits, and the number of 
digits is proportionally determined. 

All the eclipses of the moon, complete or visi- 
ble from all parts of the earth that have the moon 
above their horizon, are everywhere of the same 
size, have the game commencement and the 



so 



Arago and Lardner's Astronomy. 



same end. It is always the eastern side of the 
moon's disk that first plunges into the shadow, 
that is to say, the left side, when we look toward 
the north. 

The moon in her approach to the cone of 
shadow loses her brilliancy by insensible de- 
grees, because she then enters the penumbra, the 
intensity of which, we have seen, gradually in- 
creases up to the conical shadow. When arrived 
in this shadow, it does not usually disappear in it 
completely, even when the eclipse is total, be- 
cause it i-eceives some rays of light, that reach it 
in consequence of refraction, even within the 
cone. It has sometimes, however, been seen to 
disappear totally, when the atmosphere, loaded 
with clouds, sent it no refracted light. 

We have said that eclipses of the moon are 
visible from all points that have the moon above 
their horizon, and that they are for all these 
points of the same extent; but we must add, that 
the time when they are seen varies according to 
the longitude, and thus they furnish a means of 
determining the longitude of the place where 
they occur. Eclipses of the moon never exceed 
two hours, and may be shorter than that period. 

ECLIPSES OF THE SUN. 

When the moon interposes herself between 
the sun and the earth, the former may be eclip- 
sed. The eclipse is partial when the moon hides 
only a part of the sun's disk; total, when she 
covers the whole of it ; annular, when the sun, 



masked by the moon, projects all round in the 
form of a luminous ring ; lastly, it is central 
when the spectator's place is in the prolongation 
of the line joining the centres of the sun and the 
moon. 

The moon being nearly of the same figure as 
the earth, her shadow and her penumbra are 
formed in the same manner : only as she is much 
smaller, her cone of shadow can never cover 
more than a portion of the earth's surface. Every 
one knows, in fact, that a solar eclipse never 
takes place at the same time all over the earth, 
and it is easy to show that the same eclipse of the 
sun which is total for one point on the earth may 
be invisible at another. Only, as the moon pass- 
es before all the points of the sun's disk, she sue • 
cessively hides it from different parts of the earth 
in the direction of her motion from west to east. 
In most solar eclipses, the moon's disk is clothed 
with a faint light, proceeding from the reflection 
caused by the illuminated part of the earth. 

The apparent diameter of the moon, when it is 
at its maximum, exceeds the minimum diameter 
of the sun only by 1' 38''. Thus, the longest to- 
tal eclipse that can happen, will never exceed 
the time necessary for the moon to travel V 38'' 
of a degree, that is, about 3' 13'' of time. 

Solar eclipses, like lunar, are counted by 
digits. 

This is the manner in which the general phe- 
nomenon of eclipses takes place : — Let S be the 
sun, YY the earth, M the moon, and AMP the lat* 



Fig. 40. 




ter's orbit. If we draw the lines Wee and Vde, 
the obscure space cde, comprised between the 
lines, will be the moon's cone of shade; the 
lines VfdJi and Vcg determine the limits of the 
penumbra at abedgh. This being premised, the 
moon moves in her orbit from west to east, as 
from M to P. An observer situated at b, will 
see the eastern limb of the moon touch the 
western limb of the sun at W, and the eclipse will 
begin for him. But at the same moment the 
western edge of the moon at c, quits the eastern 
side of the sun at V, and the eclipse terminates 
for the spectator at a; there is, therefore, an 
eclipse of the sun for all the points between a 
and b : but it is evident, from the figure, that 



the sun is totally eclipsed but for a small pari of 
the earth at a time, since it is only the extremi- 
ty of the cone of shadow that reaches the earth. 
Eclipses recur only at somewhat long inter- 
vals of time : they can only happen at the syzy- 
gies: the synodic revolution of the nodes taking 
place but in 346 d 14 h 52' 16'', it is to the synodic 
revolution of the moon nearly in the ratio of two 
hundred and twenty-three to nineteen. After a 
period of two hundred and twenty-three luna- 
tions, the sun and the moon, therefore, meet in 
the same position with respect to the lunar node 
This remark serves for predicting the return o 
eclipses. Calculation has demonstrated, tha 
they occur about every eighteen years and a half. 



Arago and Lardner's Astronomy. 



SI 



As total eclipses of the sun are very rare, the 
following description, made to Halley by one of 
his friends, will not perhaps be without interest 
for the reader : 

" I send you, according to promise, my ob- 
servations of the solar eclipses, though I fear 
they will not be of much use to you. Not being 
furnished with the necessary instruments for 
measuring time, I confied my views to exam- 
ining the spectacle presented by nature under 
such extraordinary circumstances, a spectacle 
which has hitherto been neglected or imper- 
fectly studied. I chose for my point of obser sta- 
tion a place called Haradowhill, two miles from 
Amesbury, and east of the avenue of "Stone- 
henge, of which it closes the vista. In front, is 
that celebrated edifice upon which I knew that 
the eclipse would be directed. I had, more- 
over, the advantage of a very extensive prospect 
in eyery direction, being on the loftiest hill in 
the neighborhood, and that nearest to the centre 
of the shadow. To the west, beyond Stoue- 
henge, is another rather steep hill, rising like 
the summit of a cone above the horizon. This 
is Clay Hill, adjoining Westminster, (?) and sit- 
uated near the central line of darkness which 
was to set out from this point, so that I could be 
aware in time of its approach. I had with me 
Abraham Sturges and Stephen Evans, both na- 
tives of the country, and able men. The sky, 
though overcast, gave out out some straggling 
rays of the sun, that enabled me to see around 
us. My two companions looked through the 
blackened glasses, while I made some recon- 
naissance of the country. It was half-past five 
by my watch when they informed me that the 
eclipse was begun. We watched its . progress, 
therefore, with the naked eye, as the clouds per- 
formed for as the service of colored glasses. At 
the moment when the sun was half obscured, a 
very evident circular rainbow formed at its cir- 
cumference, with perfect colors. As the dark- 
ness increased, we saw the shepherds on all 
sides hastening to fold their flocks, for they ex- 
pected a total eclipse of an hour and a quarter 
duration. 

" When the sun assumed the appearance of 
the new moon, the sky was tolerably clear, but 
it was soon covered with deeper clouds. The 
rainbow then vanished, the steep hill I have 
named became A'ery obscure, and on each side, 
that is, north and south, the horizon exhibited a 
blue tint, like that it possesses in summer to- 
ward the close of day. Scarcely had we time 
to count ten, when Salisbury spire, six miles to 
the south, was enveloped in darkness. The hill 
disappeared entirely, and the deepest night 
spread around us. We lost sight of the sun, 
whose place till then we had been able to dis- 
tinguish in the clouds, but whose trace we 
could now no more discover than if it had never 
existed. 

" By my watch, which I could scarcely dis- 
cern by some light that reached us from the 
north, it was thirty-five minutes past six. Short- 
ly before, the sky and the earth had assumed, 
literally speaking, a livid tint, for it was a mix- 
ture of black and blue, only the latter predom- 
inated on the earth and at the horizon. There 
j was also much black diffused through the clouds, 
so that the whole picture presented an awful 

6 



aspect, that seemed to announce the death of 
nature. 

" We were now enveloped in a total and pal- 
I pable darkness, if I may be allowed the expres- 
sion. It came on rapidly : but I watched so at- 
tentively, that I could perceive its progress. It 
came upon us like rain falling on our left shoul- 
ders (we were looking to the west,) or like a 
great black cloak thrown over us, or like a cur- 
tain drawn from that side. The horses we held. 
by the bridle, seemed deeply struck by it, and 
pressed to us with marks of extreme surprise. 
As well as I could perceive, the countenances of 
my friends wore a horrible aspect. It was not 
without an involuntary exclamation of wonder I 
looked round me at this moment. I distin- 
guished colors in the sun, but the earth had lost 
all its blue, and was entirely black. A few rays 
shot through the clouds for a moment, but im- 
mediately afterward the earth and the sky ap 
peared totally black. It was the most awful 
sight I had ever beheld in my life. 

" Northwest of the point whence the eclipse 
came on, it was impossible for me to distinguish 
in the least degree the earth from the sky, for 
a breadth of sixty degrees or more. We looked 
in vain for the town of Amesbury, situated be- 
low us; scarcely could we see the ground under 
our feet. I turned frequently during the total 
darkness, and observed that, at a considerable 
distance to the west, the horizon was perfect on 
both sides, that is, to the north and to the south ; 
the earth was black, and the lower part of the 
sky clear; the obscurity, which extended to the 
horizon in those points, seemed like a canopy 
over our heads adorned with fringes of a lighter 
color, so that the upper edges of all the hills, 
which I recognized perfectly by their outlines, 
formed a black line. I saw perfectly that the 
interval between light and darkness, observable 
in the earth, was between Mortinsol (?) and St. 
Anne; but to the south it was less distinctly 
marked. 

" I do not mean to say that the line of shadow 
passed between these two hills, which were 
twelve miles distant from us ; but as far as I could 
distinguish the horizon, there was none behind, 
and for this reason : my elevated position ena- 
bled me to see the light of the sky beyond the 
shadow; still that yellowish green line of light I 
saw was broader toward the north than toward 
the south, where it was of a tan color. At this 
period it was too black behind us, that is, to the 
east, looking toward London, to enable me to 
see the hills beyond Andover, for the anterior 
extremity of the shadow lay beyond that place. 
The horizon was then divided into four parts, 
differing in extent, in light, and in darkness. 
The broadest and least black was to the north- 
west, and the longest and brightest to the south- 
west. The only change I could perceive during 
the whole time the phenomenon lasted, was that 
the horizon divided into two parts — one clear, 
the other obscure. The northern hemisphere 
then acquired more length, brightness, and 
breadth, and the two opposite parts coalesced. 

" Like the shadow in the beginning of the 
eclipse, the light approached from the north, 
and fell on our right shoulders. I could not, in- 
deed, distinguish on that side either defined 
light or shadow upon the earth, which I watch» 



82 



Arago and Lardners Astronomy. 



ed attentively, but it was evident that the light 
returned but gradually and with oscillation: it 
receded a little, advanced rapidly, till at last, 
with the first brilliant point that appeared in the 
sky, I saw plainly enough an edge of light that 
grazed our sides for a considerable time, or 
brushed our elbows from west to east. Having 
good reason, therefore, to suppose the eclipse 
ended for us. I looked at my watch, and found 
that the hand had traversed three minutes and a 
half. The hill tops then resumed their natural 
color, and I saw a horizon at the point previous- 
ly occupied by the centre of the shadow. My 
companions cried out that they again saw the 
steep hill toward which they had been looking 
attentively. It still, indeed, remained black to 
the southeast, but I will not say that the hori- 
zon was difficult to discover. Presently, we 
heard the song of the larks hailing the return of 
light, after the profound and universal silence in 
which everything had been plunged. The 
earth and sky appeared then as they do in the 
morning before sunrise. The latter was of a 
grayish tint, inclining to blue; the former, as 
far as my eye could reach, was deep green or 
russet. 

" As soon as the sun appeared, the clouds 
grew denser, and for several minutes the light 
did not increase, just as happens at a cloudy 



sunrise. The instant the eclipse became total, 
till the emersion of the sun, we saw Venus, but 
no other stars. We perceived at this moment 
the spire of Salisbury Cathedral. The clouds 
not dispersing, we could not push our observa- 
tions farther: they cleared up, however, consid- 
erably toward evening. I have hastened home 
to write this letter. So deep an impression has 
this spectacle made on my mind, that I shall 
long be able to recount all the circumstances of 
it with as much precision as now. After supper 
I made a sketch of it from memory, on the same 
paper on which I had previously drawn a view 
of the country. 

" I will own to you I was, methinks, the only 
person in England who did not regret the pres- 
ence of clouds: they added much to the solemni- 
ty of the spectacle, incomparably superior, in my 
opinion, to that of 1715, which I saw perfectly, 
from the top of the belfxy of Boston, in Lincoln- 
shire, where the sky was very clear. There, in- 
deed, I saw the two sides of the shadow com- 
ing from afar, and passing to a great distance 
behind us; but this eclipse exhibited great va- 
riety, and was more awfully imposing; so that 
I cannot but congratulate myself on having had 
opportunities of seeing, under such different 
circumstances, these two rare accidents of na- 
ture." 



LECTUKE XIII 



THE TIDES. 



We are now arrived at the proper place for 
explaining the phenomenon of tides. A multi- 
tude of hypotheses have been suggested, re- 
specting these regular and periodical fluctations 
of the ocean; and though their relations to the 
moon had been remarked in the remotest an- 
tiquity, it was Kepler who first demonstrated 
their dependence upon the attraction of that 
body. Newton then showed that this opinion 
is in harmony with the laws of gravitation; and 
deducing its legitimate consequences from the 
principle laid down by Kepler, he explained 
how the tides occur on the two sides of the 
earth opposite to the moon. This theory is now 
beyond all dispute. 

The waters of the ocean possess a mobility 
which makes them yield to the slightest impres- 
sions: the ocean is open on all sides, and the 
great seas communicate with each other: these 
circumstances contribute to the formation of 
tides, which owe their existence principally to 
the joint action of the sun and the moon. 

Let us first consider the action of the moon. 
It is evidently the inequality of this action which 
produces the tides; nor would there be any, if 
the moon acted equally on the whole extent of 
the ocean, that is, if it exerted equal and paral- 
lel forces on the centre of gravity of the earth, 
and on all the molecules of the waters; for then 
the entire system of the globe being actuated by 
a common movement, the equilibrium would be 
preserved. This equilibrium, then, ie only dis- jj 



turbed by the inequality and the want of pa- 
rallelism in the moon's attractions. We can 
readily conceive how her action, oblique with 
respect to those molecules of the sea which are 
in quadrature with her, and direct with respect 
to those which are directly under her, renders 
the former weightier, the latter light. In order, 
therefore, that the equilibrium be reestablished, 
the waters must rise beneath the moon, so that 
the difference in weight may be compensated 
by a greater depth. The molecules of the ocean 
situated in the corresponding point of the oppo- 
site hemisphere, less attracted by the moon than 
is the centre of the earth, in consequence of 
their greater distance, will be less disposed to 
move toward the moon than it : the centre of 
the earth, therefore, will have a tendency to re- 
cede from the molecules, which, in consequence, 
will be situated at a greater distance from this 
centre, and will be furthermore sustained at 
this height by the superior weight of the mole- 
cules at the quadratures, which communicate 
with them. 

To make this obvious by a figure, let ABCDE 
FGH be the earth, and M the moon. Attraction 
operating inversely as the squares of the dis- 
tances, the waters situated at Z will be more 
strongly attracted than those at B and F ; the 
waters at Z must, therefore, rise. On the other 
hand, the centre of the earth, 0, being nearer the 
moon than the waters at N, will be more power- 
fully attracted than they: it will therefore ap- 



Arago and Lardner's Astronomy. 



S3 




proach more to the moon, or, in other words, will 
recede from the waters at N, which will be sus- 
tained by the weightier molecules at the quad- 
ratures ; we say weightier, because the oblique 
attraction of the moon becomes decomposed and 
increases their gravity. In fact, the waters situ- 
ated at B and F, drawn by this oblique force, 
rend to approach toward O. Hence it follows, 
that there will be formed on the surface of the 
earth two menisci of waters, the one on the same 
side as the moon at Z, the other on the opposite 
side at N, which will give the earth the appear- 
ance of an elongated spheroid, the greater axis 
of which will pass through the centre of the 
earth and the moon. Hence we see that there 
would be in each place only two elevations of 
the water in a month, were it not for the earth's 
diurnal rotation. Let us see how this compli- 
i 'ares the phenomenon. 

By the earth's rotation on its axis, the more 
elevated part of the water is carried away from 
the moon in the direction of the rotation ; but 
the water still obeys the attraction it has re- 
ceived, and continues to rise after it has quitted 
its position directly under the moon, though the 
immediate action of that planet upon it be no 
longer as strong as it was. The water does not 
thus attain its utmost elevation until after the 

Fig. 42. 




moon has ceased to be at the meridian of its po- 
sition. In open seas, where the waters flow free 
ly, the moon is at p when the highest waters are 
al Z and at N. It is easy to conceive, that though 
the planet's attraction were only to cease imme- 
diately after its quitting the meridian, still tho 
ascending movement given to the waters would 
continue to accumulate them for some time; much 
more must this effect take place when the attrac 
tion only suffers diminution. 

Again, when the moon raises the waters at Z 
and N, it lowers them at B and F ; for they can- 
not rise in one place without falling in anothej-; 
and, reciprocally, it depresses them at N and Z 
when it elevates them at F and B. But by rea- 
son of the earth's rotation, the moon passes eve- 
ry day the superior and the inferior meridian of 
each place, and will, therefore, produce in it two 
elevations and two depressions of the waters, as 
actually is the case. 

Hitherto we have considered only the isolated 
action of the moon. Let us see how that of the 
sun is combined with hers. 

The attractive force exercised by the sun upon 
the earth is much greater than that manifested 
by the moon ; but as the distance of the former 
body is nearly four hundred times greater than 
that of the second, the forces exerted by the one 
upon the different parts of our planet approach 
much nearer to parallelism, and consequently to 
equality, than those of the other. And, in as 
much as it is only the inequality of the moon's 
action that produces the tides, the much more* 
equable motion of the sun must be less adapted 
to produce the same effect. Its influence in this 
respect has been calculated as about two and a 
half times feebler than the moon's. Still it is 
sufficiently energetic to produce a flux and re- 
flux ; so that there are, in reality, two tides, one 
lunar and the other solar, the effects of which 
augment or weaken each other according to the 
direction of the forces producing them. Thus, 
when the moon is new or full, that is to say, at 
the syzygies, these two bodies are in the same 
meridian, their efforts concur, and the effect must 
be the greatest possible. W hen, on toe 
contrary, the moon is in quadrature, it 
tends to raise the waters which the sun 
tends to lower, and reciprocally, so that 
the efforts of these two bodies combat- 
ing each other, the effect must be the 
least possible. 

It would seem to follow from thi*, 
that the tide should be full at the in- 
stant when the force resulting from the 
attractions of the sun and moon is ar- 
rived at its greatest intensity, b >: we 
have already seen that it is not so. hi 
fact, on the days of full moon, when the 
two bodies exercise their attraction in 
one and the same direction, the mo- 
ment of the greatest intensity of that 
action is that of their simultaneous 
passage of the meridian, or of Boon, j t : 
the tide is seldom full till some time 
after neon. Experience has sLc .vh that 
the tide which occurs on the days of 
new moon is that which has been pro- 
duced thirty-six hours previously by 
the action of the sun and moon ; it 
has been remarked besides, that at the 



84 



Arago and Lardner's Astronomy. 



Fig. 43. 




epoch, high watei always arrives at the same 
hour. Hence it has been concluded, that the 
interval of time at which the moment of high 
water follows that when the two bodies exert 
their greatest influence, is constantly the same. 
The second consequence that has been drawn 
from these two facts is, that the action of the 
sun and moon is felt in ports and on the coasts, 
by way of successive communication through 
waves and currents. We have said that, on the 
days of new and full moon, the instant when 
the two bodies exert their greatest force is that 
of the passage of the sun and moon across the 
meridian : the same is the case in the first and 
last quarter. On other days, this instant some- 
times precedes the passage, at other times fol- 
lows it, but is never far distant from it ; because, 
as we have seen, the attractive force of the moon 
is much greater than that of the sun. These 
forces, and. the tide's slowness or fastness rela- 
tively to the moon's meridian transit, vary accor- 
dingly as the two bodies recede from, or ap- 
proach the earth, as their declinations augment 
or diminish. The floods are higher, and the ebbs 
lower, at the equinoxes in March and Septem- 
ber, because then all the circumstances that in- 
fluence the elevation of the water concur to pro- 
duce their most powerful effect. 

The following are the principal circumstances 
of the phenomena of tides. The sea flows about 
six hours from south to north, swelling by de- 
grees ; it remains about a quarter of an hour sta- 
tionary, and then retires from north to south 
during other six hours. After a second repose 
of a quarter of an hour, it begins to flow again, 
and so on. 

The mean duration of theebbandflow is about 
12 h 25'; that is, half the lunar day of 24 h 50', 
the period elapsing between successive returns 
of the moon to the same point of the meridian. 
Thus the sea in every place undergoes a flux and 
reflux, as often as the moon passes the meridian, 
whether superior or inferior, of the place, that is 
to say, twice in 24 h 50'. 

These laws of ebb and flow would be perfect- 
ly in accordance with the phenomena, if the 
waters of the sea covered the whole face of the 
globe: it is not so, and it is scarcely anywhere 



but in the open seas, that they appear exactly as 
we have described them ; because the ocean is 
of sufficient .^xent to allow of the action of the 
sun and -moon taking place upon it freely. But 
these phenomena are necessarily modified in th9 
neighborhood of the shore9 by the direction of 
the winds, the situation of the coasts, and a num- 
ber of local accidents. 

Tides make themselves felt in large rivers, the 
waters of which they drive back : they are some- 
times felt as far as two hundred leagues from the 
mouth. 

Lakes have no tides, because they are too small 
to allow of the moon's action being unequally ex- 
erted upon them. Besides, she passes so rapidly 
over their surface, that there is not time enough 
to allow of the equilibrium being disturbed. 

Neither are there tides in the Mediterranean, 
nor in the Baltic, because the openings by which 
these great lakes communicate with the ocean are 
so narrow, that they cannot in so short a space 
of time receive a sufficient quantity of water 
to allow of their level being sensibly elevated. 

In the West India islands, the tides are very 
low : they seldom rise above twelve or fifteen 
inches. The anomaly may, perhaps, appear the 
more remarkable, as these latitudes, adjoining 
the equator, must be subjected to a very ener- 
getic force of attraction. But it will be readily 
conceived, that the water cannot fluctuate much 
in the neighborhood of these islands, if we re- 
flect, that the earth turning from west to east, 
the flow of the tide takes place in the opposite 
direction, and breaks like a vast wave upon the 
coast of America, which stops it, and prevents 
its passing with the moon into the Pacific Ocean. 
The winds, besides, which blow continually 
from east to west, are opposed to the ebb from 
the eastward. 

These same two causes produce a very re 
markable effect in the Gulf of Mexico. The 
winds and the tides continually impel the waters 
into this great cavity, where they accumulate 
them above the general level, and by their in- 
cessant action prevent them from falling back 
again. Thus suspended, and unable to overcome 
the forces that resist their return, these waters 
flow round the west coast of Cuba, take a nortii- 
ern direction toward the coast of America, and 
form the very remarkable current of the Gulf of 
the Floridas." So true is it that the waters accu- 
mulate in the Gulf of Mexico, that it has been 
found, by executing a series of levelling opera- 
tions across the Isthmus of Panama, that they 
rise fourteen feet higher fha£m the Pacific Ocean. 

Since the air is endowed with lightness and 
I mobility in a still higher degree than the waters, 
it must also obey the combined action of the 
sun and the moon, and there must be atmo- 
spheric tides. At first sight, however, a fact ' 
seems to militate against this conclusion, name- 
ly, that the barometer does not indicate these 
successive elevations and- depressions in the at- 
mosphere. But then it is evident the barome- 
ter ought to remain insensible to these varia- 
tions ; for the columus of air, though of different 
heights, must eveiy where be of the same weight, 
since the direct effect of the tides is, as we have 
seen, to maintain the equilibrium of the fluid, 
by compensating by height, for the diminution 



Arago mid Larchier's Astronomy. 



85 



LECTURE XIV. 

DETERMINATION OF LATITUDE AND LONGITUDE 



To determine the position of a point on any 
surface, it is necessary to know the point's dis- 
tance from two fixed lines on the surface: these 
two lines may be differently arranged, but their 
situation on the surface once fixed, it must re- 
main invariable. For the greater facility, how- 
ever, in calculation and construction, instead of 
giving these lines an inclination, ad libitum, 
they are arranged so as to form a right angle 
with each other. Thus the proceeding, which 
will enable us to fix the position of the different 
points on the earth's surface, is absolutely the 
same as that we employed to determine the po- 
sition of the stars. All we need in fact is to 
know the position we wish to fix, and its place 
in that parallel, which are, in other words, the 
latitude and longitude of the point. 

Now the latitude is found by taking the eleva- 
tion of the pole above the horizon ; for it is al- 
ways equal to that elevation. Suppose the point 
C to be distant, say thirty degrees from the 

Fiff. 44. 




equator toward the arctic pole, its zenith will 
be in CF, the great circle HOR will be its hori- 
zon; the plane of the equator EOZ will be dis- 
tant thirty degrees from the zenith F, and con- 
sequently sixty degrees from the horizon ; the 
pole P will be elevated thirty decrees, measured 
by the angle HCP. 

^ But as there is, in the other hemisphere, a 
circle presenting the same conditions, we must 
6tate whether the latitude is northern or south- 
ern. The determination of the longitude pre- 
sents more difficulty : to obtain it we measure, 
in degrees of the equator, the distance separat- 
ing the meridian of the place from another given 
meridian ; and this distance may always be as- 
certained, provided we know the hour at the 
place where the observation is made, and that 
of the place whose meridian is taken as the 
standard of comparison. For since every place 
on the earth's surface by reason of its rotation 



describes a circle, or 3G0 degrees, in twenty- 
four hours, it describes fifteen degrees in an 
hour, fifteen being the twenty-fourth part of 360 
degrees. When therefore two places are sepa- 
rated by fifteen degrees of longitude, the sun 
does not appear in the meridian of the more 
western, till one hour after it has appeared in 
that of the other ; and the latter counts twelve 
hours, when the other only reckons eleven 
hours in the morning. If the distance separat- 
ing the two places is thirty degrees, the dif- 
ference is two hours, and so on. Thus, the dif- 
ference of time being given, nothing is more 
easy than to find the difference of longitude, and 
vice versa. 

The whole difficulty then resolves itself into 
that of knowing the difference of time : a mul- 
titude of ways are employed to get at this. As 
it would be impossible for us. to describe them 
all here, we shall confine ourselves to a few 
among them. 

The exact times at which eclipses of the moon 
and o f the sun, occultations of stars by the moon, 
eclipses of Jupiter's satellites, &c, occur at a 
given meridian, are announced several years be- 
forehand. Let us suppose that a traveller, 
placed at any distance whatever east or west of 
the meridian, observes one of these eclipses or 
occultations, on recurring to his tables, he will 
find what the time is at the given meridian; and 
the difference between this time and that of the 
place where he is situated, will give him the 
longitude of that place. Observations of this 
kind may be made as often as the weather is 
clear, the phenomena which give rise to them 
being much more numerous than the days of the 
year; nor are very powerful instruments even 
requisite for this purpose: at sea, however, 
some difficulty arises from the rolling of the 
vessel. 

Marine watches, or chronometers, are of great 
assistance in determining longitude. Similar in 
construction to ordinary watches, they are only 
fitted up with extreme care, and are furnished 
with a compensator, so that they preserve the 
utmost regularity in their movements, in spite 
of the variations of temperature, and the inevita- 
ble shocks they must sustain in a long voyage. 
The chronometer is regulated at the moment of 
departure, and set exactly to the time of the 
meridian to which the longitude is to be refer- 
red. By this means the mariner has always the 
difference of time, and consequently of longi- 
tude, since he can always, by taking the time 
of the place he is in, compare it with that of the 
first meridian given by the chronometer. 

We see that this method of solving the impor- 
tant problem of longitude is so easy and simple, 
thar it would be useless ever to have recourse 
to any other, if we could always reckon secure* 
]y on the correctness of the chronometer. Un- 
fortunately this is not always the case. Modern 
skill, however, has brought these instruments U> 



Arago and Lardner's Astronomy. 



a degree of perfection that could hardly have 
been anticipated or hoped for. An idea of this 
may be formed from the following extract from 
the Elements of Natural Philosophy : " Let it 
be allowed the author of this book to make his 
readers acquainted with the surprise and plea- 
sure he experienced, after a long passage from 
South America to Asia. His pocket chronome- 
ter, and those belonging to the ship, announced 
one morning that a tongue of land marked on 
the chart, should bear fifty miles east of the ves- 
sel. Imagine the delight of the crew when an 
hour afterward, the morning fug having cleared 
off, the man on the look-out uttered the joyful 
cry, Land ! land ahead! thus confirming the pre- 
diction of the chronometers to within a mile. 
At a moment like this, one may well be struck 
with deep admiration of the genius of man. 
Compare the danger of ancient navigation with 
the confident course of our vessels, and then 
deny who can, the immense advantages of mod- 



ern art ! Had the action of a little instrument 
been in the minutest degree disturbed during a 
space of some months, its prediction would have 
been more pernicious than useful; but by day 
and by night, in calm and in storm, in heat and 
in cold, its pulsations followed each other with 
imperturbable uniformity, keeping, so to speak, 
an exact account of the motions of the heavens 
and the earth, aLd amid the waves of the ocean, 
on which the keel prints no track, it always 
marked the position of the ship whose safety 
was confided to it, the distance it had traversed, 
and that which it had yet to run." 

The meridian to which each astronomer re- 
fers his observations is entirely arbitrary, and 
varies in every nation. For a long while it was 
the general custom to take as the first meridian 
that of the island of Faro, the most western of 
the Canaries; but this custom has gradually fal- 
len into disuse, and each people now reckons 
from that which passes through its own capital. 



LECTURE XV. 

THE ATMOSPHERE.— THE HARVEST MOON. 



THE ATMOSPHERE. 

The atmosphere is that gaseous covering that 
enwraps our globe. Before inquiring into the 
influence it exercises upon the observation of as- 
tronomical phenomena, we shall do well to dwell 
for a moment on the examination of some of its 
properties. 

And in the first place, what is the height of the 
atmosphere ? This question is solved by the aid 
of one of the most valuable instruments known 
to physics, namely the barometer, whose use is 
to indicate the weight of the atmosphere. It is 
obvious that if we carry the barometer succes- 
sively to different heights, it must manifest diffe- 
rences in the weights of the columns of air at the 
different stations, and a simple proportion would 
then enable us to obtain the absolute height of 
the atmospheric stratum, if it were of the same 
density throughout. But gases being extremely 
compressible, the lower strata, which have to 
sustain the weight of all those above them, are 
necessarily more compressed, and the density of 
the atmospheric column must continually di- 
minish from the surface of the earth up to the 
highest strata. To obtain therefore equal dimi- 
nutions in the column of mercury, we must, as 
we ascend, traverse distances the greater in pro- 
portion as we mount higher. It has been proved 
by calculation, that supposing the temperature 
of the air everywhere the same, the heights of 
the mercury diminish in arithmetical progres- 
sion, while the elevations above the level of the 
sea increase in geometrical progression. But in 
operating with the barometer, we must make 
due allowance for the temperature, and for the 
hygrometrical condition of the different strata of 
the atmosphere. Its mean height has been 
estimated in this way, at from forty-four to forty- 
seven miles, its volume as the twenty-ninth of 



that of the globe, and its weight only forty-three 
thousandths. 

But what is there beyond the atmosphere ? 
Is there any fluid, or only an absolute vacuum ? 
Really we are at a loss to conceive how it is 
this question so long engaged the attention of 
scientific men ; for, in point of fact, there is no 
question admissible in the matter. How can 
the celestial spaces be void when they are filled 
with light ? Surely, whatever opinion be adopt- 
ed respecting the nature of this agent, whether 
it be a real emanation from the substance of 
luminous bodies, or a fluid put in motion by 
them, it is very evident that, upon either hypo- 
thesis, an absolute vacuum cannot exist. 

It is particularly in relation to its action on 
the luminous rays which traverse it, that the at- 
mosphere bespeaks our attention. 

We have seen in the commencement, the 
modifications that light experiences in passing 
from one medium to another, how it is refracted, 
how its rays are decomposed. 

To this property we owe the various shades 
that color the horizon at the rising and the set- 
ting of the sun. It is owing to it too, that we do 
not pass abruptly from day to night, but we are 
led gradually and with an easy transition, from 
the one to the other, by twilight and dawn. 
These two phenomena vary with the season and • 
the place. It is calculated that in our latitude, 
day does not cease eutirely, till the sun is sunk 
eighteen degrees below the horizon. 

One of the effects of atmospheric refraction is 
to alter the apparent position of the stars. The 
several strata of the atmosphere, increasing in 
density as they approach the surface of the 
earth, may be considered with' respect to each 
other as different media. The rays of light that 
traverse them, bend therefore more and more, 
as they pass from the one to the other, and as 



Arago and Lardncr's Astronomy. 



87 



the increase of density takes place by insensi- 
ble degrees, the ray of light, instead of shaping 
its course in a series of broken lines, takes a 
curved direction, the concavity of which is turn- 
ed toward the earth's surface. It will be per- 
ceived without difficulty, how the effect of this 
refraction is to make objects appear above their 
real position : for since we always refer objects 
to a place in the straight line of direction of the 
ray at the moment it enters the eye, we see 
them in this case in the prolongation of the 
tangent to the curve at the point where it enters 
the eye. Thus it is that refractiou augments 
the apparent elevation of the stars. 

ON THE MOON IN THE HORIZON. 

This is the proper place for explaining a phe- 
nomenon exhibited by the moon in the horizon : 
in that situation, the planet exhibits an elliptical 
form, and appears much larger and less bril- 
liant, than when it is in the meridian. 

To begin with the more easily explained cir- 
cumstance: it is plain that if the brilliancy of 
the moon is less vivid in the horizon than in the 
meridian, it is because the rays it sends us have 
to traverse a much thicker and denser atmo- 
spheric stratum in the former than in the latter 
position, as will appear from the figure. It is 
not surprising, therefore, that these rays should be 
weaker and more discolored, especially if we re- 
flect that in slanting along the earth's surface, they 
have to pass through a great quantity of vapor. 

As for the apparent dimensions of the moon's 
disk, this is a phenomenon that has been much 
discussed by natural philosophers. What can be 
the cause of this phenomenon, since the moon 
is more distant from us in the horizon than in 
the zenith, by the entire semidiameter of the 
earth, a difference however, to say the truth, so 
small that it cannot produce any sensible effect 
on the apparent diameter of the planet ? Gas- 
send i thought that as the moon is less brilliant 
in the horizon than in the zenith, we open the 
pupil wider on looking at it in the former sta- 
tion, and that it is for this reason we see it lar- 
ger. But that this conclusion should be valid, 
it would be necessary that variations in the open- 
ings of the pupil should produce variations in the 
dimensions of the image on the retina. Now this 




notion, wholly at variance with the principles of 
optics, is confuted by the most accurate experi- 
ments. Others have supposed, perhaps with 
more reason, that the moon's apparent increase 
of size in the horizon, is owing to our supposing 
her more distant. For, say they, two things are 
involved in the act of vision, the angle under 
which we see objects, and the distance at which 
we suppose them to be. This appreciation 
which, unknown to ourselves, we make of dis- 
tance, tends to correct the impression produced 
by the image ; and so true is this, that we can 
form a very just judgment of the height of two 
men, for instance, though they are at very un- 
equal distances, and consequently present them- 
selves under very dissimilar angles. Another 
experiment is striking. If we place an object 
in a horizontal plane, setting the eye in the pro- 
longation of this plane, then look at the object 
so as to see two images, (which will be the case, 
if we press the lower eyelid slightly with the 
fingers,) the two images will be of different di- 
mensions ; the nearer one will be smaller than 
the other, and that in proportion as it approach- 
es nearer to the eye. What proves that the dif- 
ference in the distances of the images alone 
causes the difference of their apparent dimensions 
is, that if the experiment be made so as to have 
the images on a vertical plane, it will be to no 
purpose that we separate them, they will always 
appear the one as large as the other. Now, 
continue the advocates of this mode of explana- 
tion, the moon in the horizon appears to us to 
occupy the lower portion of a dome ; it therefore 
seems to us more distant than when it is in the 
summit of the dome, that is, in the zenith. Be- 
sides, in the former situation its apparent distance 
is further increased by the comparison afforded 
by intermediate objects. Thus the erroneous 
judgment formed of the distance, modifies the 
impression produced by the image, and makes 
the star appear greater than it ought to be. 

Such is the explanation generally given in the 
present day. But without contesting the prin- 
ciple on which it reposes, we think that if the 
cause assigned concurs to produce the phenome- 
non in question, it is not the only one, and that 
there is another, the action and effects of which 
are much more evident, namely, refraction. In 
fact, the rays proceeding 
from the extremities of 
the moon's disk, reach 
the eye at an angle en- 
larged by the deflection 
the atmosphere has made 
them undergo with re- 
spect to each other : the 
planet thus seen subtend- 
ing a more open angle in 
consequence of refrac- 
tion, must therefore ap- 
pear larger. 

As to the figure it af 
fects, this again is a result 
of refraction. The moon, 
we have said, assumes an 
elliptical form, that is to 
say, its vertical is smaller 
than its horizontal diame- 
ter. This should be so ; for 
the rays proceeding from 



S8 



Arago and Lardner's Astronomy. 



the extremities of the horizontal diameter pene- 
trating the atmosphere at the same angle, are 
equally bent, butthis is not the case with the rays 
issuing from the extremities of the vertical diame- 
ter; those of theupper extremity, entering the at- 
mosphere more obliquely than those issuing from 
the lower, are more refracted, and consequently 
make the parts of the disk from which they are 
given out appear proportionally too high. This 
inequality of refraction must, therefore, alter the 
moon's figure. 

THE HARVEST MOON. 

As we are on the subject of the moon, we will 
say a word about two other phenomena it pre- 
sents. Twice a year it rises almost at the same 
hour during a week. It then takes the name of 
the harvest moon, and lune du chasseur. 

The moon, as we have seen, moves in its orbit 
from west to east. When, therefore, the earth, 
in consequence of its diurnal motion, returns 
from a meridian back again to the same, the 
moon, which has travelled in the same direction 
rather more than a thirtieth of her orbit, is fur- 
ther advanced by twelve degrees and some 
minutes ; at least such is the fact when she is in 
the equator or its vicinity : but in high latitudes 
remarkable differences take place. 

Since the plane of the equinoctial line is per- 
pendicular to the axis on which the earth per- 
forms its rotation, it is evidert that all parts of 
the equinoctial circle make equal angles with 
the horizon both eastward and westward, and 
that in equal times there is always an equal 
number of these parts above and below the 
horizon. ,If, then, the moon moved always on 
the equator, and every day gained 12° 11" upon 
the sun as she does in her orbit, she would rise 
and set fifty minutes later daily. 

But her orbit is far from coinciding with the 
plane of the equator; it approaches much more 
to that of the ecliptic, and for a moment we may 
consider them as identical. Now the different 
parts of this plane, which is oblique to the axis 
of the earth, make different angles wiih the hori- 
zon, whether to the east or to the west. The 
parts which rise with the smallest angles are 
those which set 
Fig. 46. with the largest, 

and vice versa. In 
equal times a lar- 
ger portion of the 
ecliptic rises when 
it is larger. Thus, 
let L be the lati- 
tude of London, 
AB its horizon, 
FP the axis of 
the earth, Ee the 
equator, Hk the 
ecliptic. The e- 
cliplic, in conse- 
quence of the ob- 
lique position of 
the sphere, is considerably elevated above the 
horizon of London, and makes, fig. 46, the angle 
AVK, of about sixty-two degrees and a half, 
when the sign of Cancer is in the meridian, while 
Libra is rising in the east. But when the other 
part of the ecliptic is above the horizon, that 
is, when the sign of Capricorn is in the meri- 





Fig. 47. dian, and Aries 

is rising in the 
east, the ecliptic 
makes but a very 
small angle with 
the horizon, kV 
A, figure 47, of 
about fifteen de- 
grees, that is, 
forty-seven de- 
grees and a half 
less than the for- 
mer. 

Thus the ce- 
lestial sphere ap- 
pearing to turn 
round the axis FP, a greater part of the ecliptic 
will rise in a given time when it is in the posi- 
tion in fig. 46, than when it is in that shown in 
fig. 47. 

In northern latitudes, it is when Aries' is rising 
and Libra is setting, that the ecliptic appears to 
make the smallest angle with the horizon ; it 
makes the greatest angle, on the contrary, 
when Libra rises and Aries sets. From the 
rising of Aries to that of Libra, a space equiva- 
lent to twelve sidereal hours, the angle aug 
ments; it diminishes from the setting of the one 
to that of the other. Thus the ecliptic rises 
more rapidly toward Aries, and more slowly 
toward Libra. 

But in the parallel of London, the ecliptic rises 
as much toward Pisces and Aries in two hours, 
as the orbit of the moon in six ; while she is in 
these signs, her rising is retarded but by two 
hours in six days, that is, in the mean, by twen- 
ty minutes daily : but the moon enters, fourteen 
days afterward, into the signs of Virgo and Li- 
bra, which are opposed to those of Pisces and 
Aries ; and while she is in these signs, her risings 
are daily later by about l h 15'. As Taurus, Ge- 
mini, Cancer, Leo, Virgo, and Libra, come in 
succession, the angle formed by the ecliptic with 
the horizon augments when they rise, and di- 
minishes when they set. Thus, the risings of 
the moon are more and more retarded while she 
is in these signs, and the case is the reverse with 
her settings; then the difference in the risings 
diminishes from day to day in the six other signs, 
Scorpio, Sagittarius, Capricornus, Aquarius, Pis- 
ces, Aries. 

But the moon makes the circuit of the eclip- 
tic in twenty-seven days eight hours, and takes 
twenty-nine days and a half to return to the 
same point, so that in each lunation she is at 
least once, and sometimes twice, in Pisces and 
Aries. 

Were it not that the sun appears to move in 
the ecliptic in consequence of the earth's change 
of place, each new moon would fall upon the 
same sign, and each full moon upon the oppo- 
site one ; since in the interval the moon would 
precisely make the circuit of the ecliptic : but 
as the full moon rises exactly when the sun sets, 
because when one point of the ecliptic passes 
below the horizon, the point exactly opposite 
emerges above it, it would always rise in the 
two hours of sunset in the parallel of London 
during the week when it is full. But while it 
recedes, with respect to the ecliptic, from a con- 
junction or an opposition, the sun passes to thfc 



Arago and Lardner's Astronomy. 



89 



next sign in twenty-seven days and a half. The 
moon then in the same time exceeds its revolu- 
tion, and advances much more than the sun can 
do in this interval of two days one-fifteenth, be- 
fore it can return to opposition or conjunction 
with him. We see, therefore, that opposition or 
conjunction can occur only once in any one point 
of the ecliptic. In the same way, the two hands 
of the clock are never more than once in twelve 
hours in opposition or in conjunction in the part 
of the dial they have traversed. 

Now, as the moon is full only when in oppo- 
sition to the sun, and as the latter is in the signs 
of Virgo and Libra only in autumn, the moon 
can be full in the two opposite signs of Pisces 
and Aries only in these two months. There can, 
therefore, be but two full moons in the year 
which rise during a week almost at the same 
time as the sun sets. 

When the moon is in Pisces and Aries, it may 
rise almost at the same hour in every revolution 
of its orbit, but this phenomena does not always 
attract attention when it occurs. Thus, in win- 
ter, these signs rise at noon, and the moon, which 
is then in quadrature, is not remarked. In spring, 
the sun and the moon are in these signs, conjunc- 
tion occurs, and the moon is not seen. In sum- 
mer, the rising of the moon in quadrature takes 
place at midnight, it is therefore little noticed. 
It is only in autumn that the moon, at the full, 
rises when the sun sets, which renders this phe- 
nomenon very remarkable. 

This phenomenon is as regular on the one side 
of the equator as the other. In fact, in southern 
latitudes the reasons are the reverse of those in 
northern latitudes. Thus the full moons of spring 
on one side of the equator, occur precisely in 
the signs of the full moons of autumn on the 
other side. 

Keciprocally, in spring, the full moons pre- 
sent at their setting the same phenomenon as the 
full moons of autumn at their rising. 

Hitherto, for the 6ake of simplicity, we have 
supposed the plane of the moon's orbit to coin- 
cide with that of the ecliptic, but we know that 
these planes make with each other an angle of 
from five degrees to five degrees eighteen min- 
utes, intersecting each other in the direction of 
the line of the ncdes. Now the moon passes 
twice, and often thrice, in the interval of these 
changes. In fact, as she gains almost a sign in 
the interval from one change to another, if she 
passes through a node at the epoch of change, or 
nearly so, she can return to it after having passed 
through the other before the next change. Be- 
sides, north of the ecliptic she rises sooner and 
sets later than if she moved in this plane ; the 



contrary is the case to the south. But the retro- 
grade motion of the nodes makes this difference 
vary. When the ascending node is in Aries, the 
southern half of the lunar orbit makes with the 
horizon an angle five degrees and a half less 
than that which the ecliptic makes with this 
plane when Aries rises in northern latitudes : for 
this reason, the moon rises with less difference 
of time in Pisces and Aries than if she moved 
in the plane of the ecliptic. But the descending 
node in its turn arrives in Aries in nine years and 
one hundred and fourteen days, the angle which 
the moon's orbit makes with the horizon is great- 
er by five degrees and a half; whence it follows, 
that a greater interval elapses between the sue 
cessive risings of the moon in Pisces and Aries 
than if she moved in the plane of the ecliptic. 
Hence the phenomenon of the harvest moon is 
not always equally remarkable ; its intensity va- 
ries from its maximum to its minimun? in a pe- 
riod of nine years. 

The full moon of winter is as much elevated 
above the ecliptic as the sun is in summer, and 
must, therefore, remain as long above the hori- 
zon; and, reciprocally, it remains no longer 
above the horizon in summer than the sun does 
in winter. It follows from this that the polar 
circles, which have the sun twenty-four hours 
above the horizon and twenty-four hours below 
it, must also have a full moon which remains 
twenty-four hours above, and another which re- 
mains as long below the horizon. But these 
two full moons are only those that occur about 
the tropics ; all the others have a rising and a 
setting. 

The poles have, as we shall soon see, a day of 
six months, and a night of the same duration ; 
that is, if we put out of consideration the modi- 
fications produced by refraction in the distribu- 
tion of light and darkness. Now, as the full 
moon is always in opposition to the sun, she 
cannot be seen while the latter is above the hori- 
zon, except when she is in the northern half of 
her orbit ; for when a point of the ecliptic rises, 
the opposite point sets. Thus, when the sun is 
above the horizon, the moon at the time of op- 
position is below the plane ; it is, therefore, in- 
visible half the year. But when the sun is sunk 
below the horizon, the full moon is visible to 
those places he no longer illuminates. Thus the 
poles which are deprived of the moon in sum- 
mer, that is to say, when they have the sun, be- 
hold it again in winter when he has quitted 
them. They are never, therefore, in deep dark- 
ness, since they enjoy, for the most part, the 
moon's light as a compensation for the long ab- 
sence of the sun. 



LECTURE XVI. 



THE SEASONS AND THE DAYS. TEMPERATURE— WINDS. 



THE SEASONS AND TRE DAYS. 

We have already seen that if the axis on which 
the eardi turns were perpendicular to the plane 
of the ecliptic, the days and nights would be of 



equal duration in all parts of the globe ; but the 
inclination of the planes of the equator and of 
the ecliptic is twenty-three degrees twenty-eight 
minutes, and this it is that produces the diversi- 
ty of the seasons and of the days. 



90 



Arago and Lardner's Astronomy. 



And, in the first place, it is easy to compre- 
hend the variety exhibited by the phenomena of 
day and night in different parts of the earth. 

At Paris, for instance, the latitude is about 

forty-eight degrees. This will give, therefore, 

for the zenith Z, Bk will be the horizon, Fp the 

line ui the poles, and Ee the equator. When 

the sun, S, is in the 



Fiff. 48. 




plane of the equa- 
tor, it will describe 
the circle Ee, di- 
vided by the hori- 
zon HA, into two 
equal parts ; it will, 
therefore, be a8 long 
, above as below this 
"■ plane, and the days 
will be equal to the 
nights. But when 
the sun ahall have 
declined 23° 28' to- 
ward the south 
pole, or, in other 
words, when he shall have attained the tropic of 
Capricorn, he will describe the circle S'M, di- 
vided by the horizon H/t, into two equal parts, 
the greater of which is below this plane. The 
nights will, therefore, be longer than the days. 
Lastly, when the sun shall have reached twenty- 
three degrees and twenty-eight minutes of north- 
ern declination, it will be in the tropic of Cancer, 
will describe the circle S"n, and the days will 
be longer than the nights. 

Let us now see what takes place in the equa- 
torial regions. For there the zenith, Z, coincides 
with the equatorial 
Fig. 49. plane, Ee, and the 

horizon Hh, with 
the axis of the poles 
Pp. Now the sun, 
whether he be at 
S, S', or S", that is 
to say, at the equa- 
tor or at the tropics, 
always describes 
circles which the 
horizon divides in- 
to two equal parts. 
The equatorial re- 
gions, therefore, 
have always days 
and nights of equal 
duration. 

The polar regions, on the contrary, have for 
the line of their zenith Z, which coincides with 
that of their poles 




Fiff. 50 




Pp, and their ho^ 
rizons, H h, be- 
come identified 
with the equator 
Ee. When the 
sun, S, is in the 
plane of the equa- 
tor, it describes 
the circle S H, 
which is that of 
the horizon, and 
the half of its 
disk is above this 
plane, while the 
other half is be- 



ZS" 



NA 



low it. But when the sun, S",has reached the tro- 
pic of Cancer, it describes the whole circle, S"N, 
above the horizon, whereas, at the tropic of Cap- 
ricorn, it describes the circle S'M, which is whol- 
ly below it. The polar regions, therefore, have the 
sun six months above and six months below the 
horizon, that is, a day and a night each of six 
months. Still they are not plunged in profound 
darkness during the absence of the sun, for we 
have already seen that, independently of the 
twilight they enjoy till the sun is sunk eighteen 
degrees below the horizon, the moon too gives 
them light in the absence of the greater lumi- 
nary. We may add, that twilight must be more 
intense here than elsewhere ; the rapid diminu- 
tion in the density of the air at small elevations, 
on account of the habitual congelation of the 
earth's surface, is one of the causes assigned as 
necessarily producing extraordinary degrees of 
refraction in these regions. 

Lastly, at the polar circles, the zenith coin- 
cides almost with the tropics. When, therefore, 
the sun, S, is in the plane of the equator, and 
describes the cir- 
Fig. 51. cle SE, divided 

by the equator 
into two equal 
parts, the days 
will be as long 
as the nights. — 
But when it is 
in the tropic of 
Cancer, it will 
describe the cir- 
cle S"N, and will 
only brush the 
horizon with its 
lower edge ; the 
day will, there- 
fore, be 24 hours 
long. When, on the contrary, arrived at the 
tropic of Capricorn, it traverses the circle S'M, 
it will remain 24 hours below the horizon, which 
it will touch with its upper edge. 

In this explanation we have supposed that the 
sun turns round the earth, whereas it is the earth 
turns round the sun ; but the result is absolutely 
the same. To combine, however, the explana- 
tion of the real with that of the apparent phe- 
nomenon, we will make the earth turn round 
the sun in speaking of the seasons. 

Let then S be the sun, T the earth, ST the ra- 
dius connecting their centres, or the radius vec- 
tor. This radius meets the surface of the earth 
at A. All the points situated in the parallel AB 
will, therefore, have the sun successively in their 
zenith as the rotary motion carries them to A, 
and these regions will then have summer. If 
the point A is the summer solstice, the paral- 
lel described by the earth's rotation will be 
the northern tropic ; and in this position the 
plane PTS is perpendicular to that of the eclip- 
tic. 

But when, in consequence of the earth's 
change of place, it arrives at the point diametri- 
cally opposite, that is, at T', the radius vector 
will meet the earth's surface at A', and the pa- 
rallel A'B', which, in the former position, re- 
ceived the most oblique rays, will now receive 
them vertically, and the regions it includes will 
have summer, while those of the opposite tropic 




Arago and Lardner's Astronomy. 



91 




will have winter. The plane ST'P', determined 
by the meeting of the radius vector and the 
axis, is here too perpendicular to the ecliptic, 
as in the preceding case; but the angle STP, at 
which the radius vector and the axis of the earth 
intersect in the former situation, is acute, while 
in this it is obtuse, STT'. In the intermediate 
positions it is a right angle. It therefore in- 
creases from T to T" and decreases from T' to T. 

Lastly, when the radius vector is perpendicu- 
lar to the axis of the earth at the points t and t', 
and the sun appears to describe the equator, the 
equinoxes take place, that is, the days and nights 
are equal all over the earth, and it is either 
spring or autumn. 

The space included between the tropics is 
called the torrid zone, because the sun's rays 
almost always falling there perpendicularly, the 
heat is excessive. 

The regions which extend from the tropics to 
the polar circles, enjoy a moderate temperature, 
and are called temperate zones. 

Lastly, the unknown regions comprised be- 
tween the polar circle and the poles, constitute 
the frigid zones. 

We may illustrate, by a very easy experiment, 
the manner in which 
the combined motions 
of the earth round its 
axis, and, in space, pro- 
duce the phenomena 
of days and seasons. 

Take a stiff rod, of 
iron for instance, and 
bend it into a circle, 
as represented in the 
figure : seen sideways, 
this rod will appear an 
ellipse. Place in the 
centre a lighted can- 
dle; then fasten a silk 
thread to the pole of 
a terrestrial globe of 
about three inches di- 
ameter, and twisting 
the thread, so that, 
when it untwists, it 
may make the globe 
turn from west to east; 



if you place it against the circle, you will see light 
and shadow succeed each other upon its surface, 
and imitate the regular succession of day and 
night. But, while the globe turns, if it be made 
to pass along the circumference of the circle, its 
centre being always in [the plane of ] this circum- 
ference, the candle, which is perpendicular to 
the equator, illuminates the globe from one pole 
to the other, and every part of it is alternately 
light and dark, thus making a perpetual equinox. 
Thus we should always have days and nights of 
equal duration, without variations of seasons, if 
the axis of the earth was perpendicular to its 
orbit. But this is not the case. Let us, there- 
fore, incline the circle on which the globe turns, 
to the latter's axis, in the direction ABCD for 
instance. If we place the globe in the lowest 
part of the circle H, and make it turn upon itself 
and round the circle, in the direction from west 
to east, the candle will perpendicularly illumi- 
nate the tropic of Cancer, and the north pole 
will see the light. From the equator to the po- 
lar circle, the days will be longer than the 
nights ; the contrary will be the case in the other 
hemisphere. The sun will never set for the 
northern frigid zone, and never rise for the 
southern. But when the revolving motion shall 
have carried the globe from H to E, the limit of 
shadow will approach the northern, and recede 
from the southern pole: the places adjoining the 
former will be les^and less illuminated, and the 
contrary will be the case with the latter. The 
days, therefore, decrease to the north, and in 
crease to the south, as the globe moves from H 
to E. When it is at this point, the candle is in 
the plane of the equator, the limit of shadow 
stops exactly at the two poles, and the day3 are 
everywhere equal to the nights. Lastly, when 
the globe is at F and G, we see the same phe 
nomena take place in an inverse order. 

THE EARTH'S TEMPERATURE. 

The micrometer, in accordance with what we 
know of the position of the earth at different 
seasons of the year, teaches us that the sun is 
nearer us by one thirtieth in winter than in 
summer. The temperature of this latter season 
is, notwithstanding, much more elevated than 

Fig. 53. 




92 



At ago and Lardner's Astronomy. 



that of the former. What are the causes of this? 
There are three principal ones. First, the physi- 
cal constitution of the atmosphere, which varies 
in these two seasons. In summer, the atmo- 
sphere is generally dry, but in winter it is loaded 
with vapors, and considerably weakens the in- 
tensity of the sun's rays. The second cause is, 
the obliquity of the sun's rays in winter : and we 
know that they are reflected in proportion to 
this obliquity, and that those that are reflected 
do not warm. Lastly, and this is the principal 
cause, the sun in summer remains much longer 
above the horizon than in winter. The night, 
the period when caloric is lost, is shorter, and 
the day longer. An idea may be formed of the 
effect capable of being produced upon tempera- 
ture by the difference between the days and 
nights, when we say it has been calculated, that 
were the sun in summer to remain ten days be- 
low the horizon, it would be enough to freeze 
everything on the surface of the earth. 

On an average, the temperature rises from the 
5th of January to the 5th of July, and falls from 
the 5th of July to the 5th of January. 

The mean temperature of the equator is from 
80° to 82° ; but it is remarked, that the southern 
hemisphere is much colder than the northern: 
the reason is, that the former is in a great part 
covered with water. Now we know that water 
does not heat so easily as the earth, a great part 
of the caloric incident upon if being incessantly 
absorbed by evaporation, freezing and melting 
of ice. It has also been remarked that the west- 
ern shores of continents are much warmer than 
the eastern : this is an effect of the winds, and 
of the general position of the seas. In our coun- 
tries, as in America, the westerly winds pre- 
dominate ; and these winds, blowing from off 
.sea, are always mild in temperature, for the tem- 
perature of the sea is never very high nor very 
low ; and this may easily be conceived : the mo- 
bility of the liquid mass, and its constant tend- 
ency to a state of equilibrium, never permitting 
a superficial layer to cool very much compara- 
tively with the rest. As soon as the temperature 
falls, its weight becoming augmented, it de- 
scends into the mass, and another layer takes its 
place. 

Does the earth possess heat of its own, or does 
all it owns reach it from the sun ? This latter 
opiuion, which has been mentioned by some 
philosophers, can no longer make head against 
the facts at present known. We know that, at a 
certain depth, the temperature, independently 
of the action of the sun, remains continually in- 
variable, and experiments have ascertained that 
it rises in proportion as we descend to greater 
depths: the law of this progression is almost a 
degree for every ninety feet. 

Whatever may be the cause of this proper 
temperature of the earth, whether it proceed 
from the primitive incandescence of our planet, 
or from the incessant action of calorific 'and 
electrical agents existing in nature, we can dem- 
onstrate that this temperature has not changed 
for, at least, many thousands of years. In fact, 
had the temperature of the earth at remote pe- 
riods been either higher or lower, its volume, 
from the effect of dilatation or contraction, 
would have been greater or less But then the 
medium of the moon must have varied. Now 



this is not the case, for the duration of the side- 
real day is now exactly what it was in the most 
remote times. 

We have seen that the temperature rises in 
proportion as we descend into the interior of the 
soil ; it follows a contrary progression in propor- 
tion as we rise above the level of the sea. In 
the most usual condition of the atmosphere, we 
find that the temperature decreases equably with 
the increase of elevation in all climates, when 
we begin our reckoning from one and the same 
lower temperature ; but the law of progression 
changes with the point of departure. So that in 
the temperate zones, for instance, according to 
Saussure's observations, the rate is 1° of the ther- 
mometer for 144 yards of elevatiou in winter, 
and 98 yards in summer : there is, therefore, 
an elevation at which the progressive cooling 
reaches the term of ice ; hence the existence of 
eternal snow on lofty mountains, and the unequal 
elevation of the point at which it commences in 
differentclimates. The vertical decrease of tem- 
perature varies also with the seasons, the expo- 
sure of the situation, and even the more or less 
| transparent state of the sky. 

One of the most interesting labors of the age 
is the important application made by V. Hum- 
boldt, of the geography of plants to the mean 
temperature of their places of growth. This 
celebrated traveller has determined in a general 
manner the elevation and the temperature of 
the zones, in which every plant seems best to 
thrive. Every vegetable can only live within 
certain determinate limits of temperature, and the 
proximity of these limits is indicated by the more 
or less stinted appearance of its growth. The 
aspect of the vegetables growing in each coun- 
try presents, therefore, as it were, a sort of living 
thermometer, pointing out to the traveller their 
mean annual temperatures and their extremes. 

In general it will readily be conceived, that, 
in so vast and so movable a mass as the atmo- 
sphere, the slightest causes of agitation may pro- 
duce the greatest and the most durable pertur- 
bations. We see, therefore, that such effects 
must frequently result from the small local per- 
turbations occurring in temperature, and that 
the greatest and most constant must result from 
the annual and diurnal motions, and also from 
the more or less energetic influence exerted by 
the sun upon the earth in the different seasons. 
Such are, probably, the most ordinary causes of 
those frequently long enduring agitations produ- 
ced in the atmosphere, which are called toinds. 

The most remarkable are those which blow 
regularly between the tropics, and which are 
called trade-winds. We borrow from the Ele- 
mens de Philosophic Naturelle, the very complete 
explanation they give of them. 

If the terrestrial globe were at rest, and the 
sun's rays were always directed upon the same 
surface," the column of air situated above that 
surface would be heated to a high degree, and 
all the layers of that column would ascend suc- 
cessively, like oil, to the surface of water, or aa 
smoke mounts in a chimney strongly heated, 
while currents of air, or winds, would constantly 
flow in from all the lower parts toward the cen- 
tral surface. But the earth is continually in mo 
I tion upon itself, and round the sun ; the middle 
I! region, the equatorial belt or zone, may, there 



Arcigo and Lardner's Astronomy. 



93 



fore, be assimilated to the surface supposed in 
the preceding hypothesis; it is the part on 
which the sun has continually shed his beams 
since the beginning of time : there ought con- 
stantly to have been, and, therefore, there al- 
ways have been currents toward this zone, some 
setting in from the southern part, some from the 
northern. Such is the cause of those trade- 
winds, on which mariners count as securely as 
on the periodical return of the sun, in most of 
the situations comprised between the thirtieth 
degrees of northern and southern latitude. 

These winds, however, do not appear to sweep 
the earth in the directions of the meridians, that 
is, they do not appear to blow from due north 
and due south : this proceeds from the earth's 
rotation on its axis, which taking place from 
west to east, gives the north winds the appear- 
ance of blowing directly from the northeast, and 
the south winds that of blowing directly from the 
southeast. These appearances may be easily 
understood from the following facts. When the 
atmosphere is perfectly calm, a horseman gallop- 
ing over the plain seems to feel the wind blow- 
ing directly against his face with great force. If 
he gallop toward the east, and the wind blows 
directly from north or south, the two-fold sensa- 
tion he experiences is compounded into a mixed 
resulting sensation ; and in the first case, the 
sound will seem to him to be direct from the 
northeast, in the second, direct from the south- 
east. Another experiment: — Cause a sphere 
to revolve on a vertical axis, and let a small ball, 
or, better still, a jet of water, roll from the supe- 
rior pole : the ball or the water will not imme 
diately acquire the velocity of the globe, but 
they will tend to descend by the shortest line 
from the pole to the equator of the sphere. Still 
the trace marked by the liquid on the surface of 
the sphere will not be a meridian, but an oblique 
line, which were it prolonged, would not pass 
through the inferior pole. It is thus the rotation 
of the earth gives the trade-winds a direction 
toward the west, and it is not, as sometimes 
said, because the sun draws them along, that 
they have this direction. 

We know that on the limits within which they 
prevail, that is to say, at about thirty degrees 
north and south from the situation of the sun, 
these winds seem to set in almost directly from 
the east, whereas, in proportion as we approach 
the central line, they strike ships more directly 
from north to south, and from south to north. 
This is owing to the fact, that on arriving at the 
extreme parallels, the cold air, as it acquires 
heat, dilates, and rises before it has acquired the 
rotary velocity of the zone it occupies ; it moves 
with less rapidity than it, and the bodies placed 
in its zone, strike the air from west to east with 
the whole excess of their velocity, and the result 
is the same as if, the earth being motionless, the 
wind blew constantly on these bodies. In pro- 
portion, however, as the currents of air proceed 
on their way, they partake more and more of the 
velocity of the earth's rotation, and at last have 
almost completely acquired it by the time they 
arrive at the central line in the middle of the 
zone of sixty degrees ; thus the wind from the 
east becomes less and less felt in proportion as 
we approach this line, at which it is much less 
sensible. Such would be the condition very 



nearly of a fluid poured on a wheel turning hori- 
zontally, and which should approach more and 
more from the centre toward the circumference. 
Arrived at the points adjacent to this limit of the 
circle, it would not yet have acquired all its ve- 
locity, but the continual rotation would at last 
communicate it completely to it, the fluid would 
then be in motion like the circumference, but 
it would be in a state of relative rest with re- 
spect to it. It must be understood, that we do 
not here take into account the influence of the 
centrifugal force. 

While the dense air of the polar regions pre- 
cipitates itself toward the equator, to fill up the 
vacuum formed there, and thus gives rise to the 
trade-winds, that which the permanent action 
of the sun has dilated and elevated, must neces- 
sarily form a counter-current in the upper re- 
gions of the atmosphere, which will proceed in 
an opposite direction to dispose of its charge of 
heat. This actually takes place : and this phe- 
nomena, anticipated by theory, has been con- 
firmed by observation. Thus it has been ascer- 
tained that the summit of the Peak of Teneriffe 
is constantly assailed by a violent wind, blowing 
in a contrary direction to those trade-winds that 
swell the waves of the ocean at its feet. Thus, 
in 1812, the volcanic dust discharged from the 
island o,f Saint Vincent, passed in a thick cloud 
across Barbadoes, to the great astonishment of its 
inhabitants, and &11 at more than a hundred 
miles distance, after having accomplished this 
long journey in a direction contrary to the violent 
winds, from which ships can only escape by a 
lengthened deviation from their course. Thus, 
in the voyage from the Cape of Good Hope to 
Saint Helena, the light of the sun is often for 
many days eclipsed by a mass of thick clouds, 
moving southwards at a great elevation in the 
atmosphere. These clouds are nothing else than 
watery vapors, that have risen from beneath the 
equator with the heated air, and which again 
become condensed on approaching the colder 
regions of the southern hemisphere. 

Without the tropics, where the solar influence 
is much weaker, the winds are occasionally sub- 
jected to other causes, unfortunately at present 
but imperfectly known. Much less regular in 
the temperate regions, they are called variable 
winds : still we may regard as a general rule, 
applicable as well to the one class as to the 
other, what we have said of the trade-winds, 
viz. that the air, in passing toward the equatorial 
regions from the northern or southern poles, 
where it was at rest; must produce the effect of 
an easterly wind, or a wind opposed to the diur- 
nal motion, until it has acquired the velocity of 
the zone over which it blows ; and reciprocally, 
that the air heated in the equatorial regions, and 
elevated to the higher parts of the atmosphere, 
where it has acquired almost a corresponding 
velocity, falling back to the poles with this ex- 
cess* of velocity from west to east, must strike 
the bodies it encounters in the same direction. 

These west winds, in a great number of situa- 
tions without the tropics, are almost as regular 
as the winds in the intertropical zone ; they are 
as well entitled as the latter to the name of 
trade-winds, so much do they abridge the pas- 
sage from New-York to Liverpool, compared 
with that in the opposite direction from Liver 



94 



Arago and Lardners Astronomy. 



pool to New- York. Thus in the northern hemi- 
sphere, the due-north wind produces the affect 
of a northeast wind, and the due-south wind be- 
comes a southwest wind. Eugland is exposed 
to these wiuds three hundred days in the year. 
These phenomena, of course, are inverted in the 
southern hemisphere. 

Lastly, we will conclude this meteorological 
digression, by mentioning two other winds, 
which blow regularly on the coasts, and which 
are known by the names of land-breeze and sea- 
breeze. 

When the sun is sunk below the horizon, the 
land and the water, which his presence had 
heated, lose their caloric by way of radiation, 
but the loss experienced by the surface of the 
land is much more rapid and more considerable, 



than that sustained by the surface of the water. 
The strata of air which rest on these two surfaces 
must consequently be differently cooled, and 
soon the air which rests upon the soil, being 
colder and denser than that over the sea, must 
precipitate itself into the place occupied by the 
latter. This occurrence takes place toward the 
end of the night, and constitutes the land- 
breeze. 

But when the sun has reappeared above the 
horizon, its rays heat the surface of the soil much 
more rapidly than the mass of the waters, and 
the air that hangs over them must be much 
more heated and dilated on land than at sea. At 
the close of day, the colder and more condensed 
air will blow in toward the shore, and produce 
the sea-breeze. 



LECTUEE XVII. 



THE CALENDAR. 



A calendar, so called from the Roman cal- 
ends, is a table showing the divisions of fime by 
days, weeks, months, seasons, and years. We 
6hall take a rapid review of the principal ones 
that have been employed by different nations. 

The opinion of the learned is, that the year of 
the Egyptians and the Persians consisted of 365 
days, so that every four years they lose a day in 
the solar year, and after a period of 1460 years, 
called the Sothiac period, or great canicular 
year, the civil and the solar year recommenced 
at the same time. The 365 days of the year 
composed twelve months, each of thirty days, 
and the five remaining days were added under 
the name of epagomence, or complementary days. 
This was the calendar adopted as a model by the 
French republic. 

The Greeks had at first a year of 360 days, di- 
vided into twelve months of thirty days "each : 
after a period of two years, which they called 
trieteris, they intercalated a month of thirty days, 
so that they had alternately a year of 360, and 
and one of 390 days. They reckoned in this 
way until about the sixth century of our era. At 
this epoch, some progress having been made in 
astronomical acquirements, it was found that the 
moon accomplished her revolution in twenty- 
nine days and a half; this period was doubled 
to make two months, one of thirty days, the other 
of twenty-nine, which commenced with the new 
moon, or the neomenia. But as the twelve 
months made but 354 days, the remaining eleven 
days and a half were added during a period of 
eight years, called an octaereis, and formed three 
intercalary months of thirty days, placed in the 
third, the fifth, and the eighth years of*this pe- 
riod. This manner of counting was in very good 
•accordance with the course of the sun ; but the 
Athenians, who made this reform, had learned 
from the oracle, that the year ought to be regu- 
lated by the course of the sun, and the months 
and the days by that of the moon. The civil , 
year, such as they had arranged it, agreed well j| 
enough with the commands of the gods, but the I! 



second part of the injunction was not complied 
with. In fact, after an octaereis, the moon had 
still a day and a half to accomplish her revolu- 
tion. After two octaereids therefore, three com- 
plementary days, or epagomence, were added ; 
and thus they found themselves in accordance 
with the moon, but they were no longer so with 
the sun. 

To solve the difficulty, Meton, a celebrated 
astronomer, imagined a period or cycle of nine- 
teen years, which conciliated the motion of the 
sun and moon, by embracing a complete num- 
ber of revolutions of those two bodies. This 
period was composed of 235 lunations, viz. 228 
at the rate of twelve to the year, and seven 
others for the eleven days, by which the solar 
exceeded the lunar year. The seven lunar 
months, of which six were of thirty days each, 
and the seventh of twenty-nine, were called em- 
bolismic months. This arrangement appeared so 
admirable to the Greeks, that when it was pro- 
posed at the Olympic games, it was received 
with acclamations, and adopted by all their 
colonies. The calculation of it was exhibited in 
letters of gold in the public places for the use of 
the citizens : hence comes the name of the gold- 
en number, under which it still figures in our 
calendars. Meton's cycle, however, was not 
perfectly exact ; for after seventy-six years, the 
calendar was found to be a day in advance of the 
moon's course. 

The Arabic calendar, which is that of the Ma- 
hometans, is exclusively based on the course of 
the moon. The first day of each month always 
corresponds to new moon. But the years of this 
calendar are very vague ; they run successively 
in a retrograde course through all the seasons of 
the year. 

Let us pass on to the Koman calendar. Little 
is known of what it was before Julius Caesar, 
who reformed it. To this effect, having learned 
from an Egyptian astronomer,, that the solar year 
consisted of 365£ days, he made the civil year 
365 days, and added a sixth at the end of four 



Arago anci Lardner's Astronomy. 



95> 



years for the quarter of a day dropped. This 
fourth year, which continued 366 days, was called 
bissextile. The months, twelve in number, con- 
sisted of thirty and thirty-one days, except that 
of February, which bad twenty-eight in ordina- 
ry years, and twenty-nine in bissextile. The 
Romans divided their months into three epochs : 
the calends, which fell on the first day of the 
month ; the nones, which were the fifth ; and the 
ides, which arrived the thirteenth. The year 
fixed by this calendar was called the Julian 
year. 

This year, however, was too long by eleven 
minutes nine seconds, an error amounting to a 
day in about 135 years, and the council of Nice 
having in 3*25 fixed Easter for the 21st of March, 
the day of the equinox, this festival, in 1582, had 
gone back to the 11th of the same month. To 
remedy this inconvenience, Pope Gregory XIII. 
published a bull, cutting off ten days from the 
year 1582, and commanding to reckon the 5th of 
October as the 15th. To prevent the return of 
a similar error, another modification was made. 
Up to that time, the intercalary day had regular- 
ly been added to February every four years ; it 
was ordered that in the space of 400 years three 
bissextile years should be cut off, so that at pre- 
sent, the bissextile years are all those, the index 
of which is divisible by four, and when this is a 
secular year, it is necessary that the significant 
figures of the index, that is to say, the index of 
the century, should be divisible by four. Thus 
1600 was bissextile, 1700 and 1800 were not so, 
nor will 1900 be so, but 2000 will. The error 
thus corrected is actually so small, that it may 
without inconvenience be neglected for several 
thousand years. 

Such is the Gregorian calendar, or the new 
stole. It is now adopted by almost all Christen- 
dom. The English did not adopt it till 1752, and 
their 3rd of September was carried on to the 
14th, the Julian calendar presenting at that 
epoch an error of eleven days. At present, none 
follow the Julian calendar in Europe, but the 
Russians, and the Christians of the Greek church, 
whose year begins twelve days later than ours. 
This is the cause of the difference we perceive 
between our dates and theirs. 

The months are divided into weeks. Among 
as the week consists of seven days, namely, 
Lundi, Mardi, Mercredi, Jeudi, Vendredi, Same- 
di, Dimanche (Sunday), names derived from 
those of the planets* : thus Lundi is the moon's 
day (Luna), Mardi that of Mars, Mercredi that 
of Mercury, Jeudi that of Jupiter, Vendredi that 
of Venus, Samedi that of Saturn, and Dimanche 

*The French names of the week days generally pre- 
serve more resemblance to the Roman than do the Eng- 
lish. Our Teutonic ancestors translated the Roman 
names, substituting their own deities, as Wodin, Thor, fee. 
for Mercury, Jove, &c— Trans. 



that of the Sun, as their etymology indicates in 
other languages. But what we should not hava 
discovered, if historians had not communicated 
it to us, is the order in which these planets gave 
their names to the days of the week. The an- 
cients classed the planets, or at least the stara 
which they considered as such, according to the 
duration of their revolution ; thus Saturn, Jupi- 
ter, Mars, the Sun, Venus, Mercury, and the 
Moon. Now this is the way in which the names 
of the planets have come to be affixed to the days 
of the week in their present order. The first 
hour of Saturday for instance, was consecrated 
to Saturn, who for this reason gave his name to 
the day : the second hour was consecrated to 
Jupiter, the third to Mars, the fourth to the Sun, 
the fifth to Venus, the sixth to Mercury, and the 
seventh to the moon ; then the eighth to Saturn, 
and so on, till the twenty-fourth hour, which in 
following this coui-se came to be consecrated to 
Mars. The first hour of the following day was 
consecrated to the sun, which follows next, and. 
the day took its name : the second hour was con- 
secrated to Venus, and so on. By pursuing this 
in detail, it will be seen that each day of the 
week in turn took its name from the planet to 
which its first hour was consecrated. 

It now remains for us to say some words of the 
terms employed in calendars. 

Th2 solar cycle is a period of twenty-eight 
years, after whic^ the days of the week return ra 
the same order, and at the same day of the 
month, while the bissextile years follow regu- 
larly every four years. The bissextile years also 
recommence, at the termination of the solar 
cycle, the same course with respect to the days 
of the week on which fall those of the months. 
The solar cycle owes its origin to the fact that 
the year does not contain an exact number of 
weeks, since it consists of fifty-two weeks and 
one day. This cycle would therefore be only 
of seven years (since in that period the extra day 
of each year would make a week) if there were 
no bissextile years ; but as there is one every 
four years, the cycle cannot be complete with- 
out continuing seven leap years, so that the extra 
day of each of these may give a week. 

We have already spoken of the lunar cycle, 
the year of which is called the golden number. 
It is a period of nineteen years, after which the 
sun and the moon meet again in the same position 
or nearly so, since the conjunctions, oppositions, 
&c. of these bodies are within an hour and a half 
the same as at the beginning of this period on 
the same days of the month. 

Since the solar and the lunar years do not re- 
commence together till after nineteen years, 
there is in this interval an excess of the former 
over the latter. It is this number of days by 
which the solar year exceeds the lunar, that id 
designated by the name of epact. 



APPENDIX. 



TABLE OF THE CONSTELLATIONS, 

With the Number of Stars in each, as far as those of the Sixth magnitude. 



* Thus marked are modern. 



ZODIACAL CONSTELLATIONS. 



NAME 
OF CONSTELLATIONS. 



Aries . . 
^< Taurus 



Gemini 

* Cancer 

Leo with Coma Bere 

nices 

Virgo 

Libra 

Scorpio 

Sagittarius 

Capricornus 

Aquarius • 

Pisces 



No. of 
Stars 



141 

So 



95 
110 
51 
44 
69 
51 
108 
113 



Principal Stars. 



Aldebaran 

Castor and Pollux 



Regulus 

Spica Virginis. 
Zubenich Meli 



Antaaes 



Scheat. 



NORTHERN CONSTELLATIONS. 



Ursa Minor, the Lesser) 

Bear 

Ursa Major, the Great 

Bear 

Perseus 

Auriga, the Waggoner 

Boe'tes 

Draco 

Cepheus 

*Canes Venatici, viz. 
Asteria and Chara, 

the Greyhounds 

*Cor Caroli 

Triangulum 

*Triangulum minus ..... 

*Musca 

*Lynx 

*Leo Minor 

*Coma Berenices 

*Camelopardalus 

*Mons Menelaiis 

Corona Borealis 

Serpens 

*Scutum Sobieski 

Hercules cum Ramo et 

Cerbero 

Hercules or Eugonasia 
Serpentarius or Ophiu- 

cus 

*Taurus Poniatowski — 

Lyra 

* Vulpeculus et Anser 
the Pox and Goose . 

Sagilta 

Aquila, the Eagle with 

Antinous 

Delphinus 

Cygnus, the Swan... 
Cassiopeia, the Lady in 

her chair 

Equulus, the Horse 

Head 

*Lacerta v 

Pegasus -^.. • 

Andromeda v^. . 



113 

74 
7 

22 

37 
13 

71 

IS 
81 



Pole Star. 



Dubhe 

Algenib • . • 
Capella... 
Arcturus. . 
Rastaber. . 
Alderamin. 



Ras Algratha. 
Ras Aliagus.. 
Vega 



Allan 

Dereb Adige . 



Markab 
Almaac . 



SOUTHERN CONSTELLATIONS. 



NAME 
OF CONSTELLATIONS. 



No. Of 
Stars. 



'Phoenix 

*Officina Sculptoria.. 

Eririanus 

*Hydrus, the Water 
Snake , 

Cetus, the Whale 

+ Fornax Chemica 

*Horologium 

*Rheticulus Rhomboid 

alis 

*Xiphias Dorado, the 

Swordfish 

*Celapraxitellis 

Lepus 

* Columba Noachi 

Orion 

Argo Navis, the Ship... 

Canis Major 

*Equuleus Pictorius 

*Monoceros 

Canis Minor 

*Chamaeleon 

*Pyxis Nautica 

*Piscis Volans 

Hydra 

"Sextans 

*Robur Carolinum, Roy 

alOak 

*Machina Pneumatica.. 

Crater 

Corvus. 

*Croziers, Cruzero..... 

*Apis Musca 

*Apus, or Avis Indica 

Bird of Paradise.... 

*Circinus, the Compass. . 

Centaurus 

Lupus 

*Q,uadra Euclidis 

^Triangulum Australe.. 

Ara, the Altar 

*Telescopium 

Corona Australis 

*Pavo, the Peacock 

*Inus •_ 

*Microscopium 

*Octans Hadleiensis 

Grus, the Crane 

"^Toucan 

Pise is Australis 



Principal Stars. 



Achernar 



Menkar 



Betelgeuse 
Canopus • . 
Sirius 

Procyon. . . 
Cor Hydrae 

Alker 

Algorab . . . 



Fomalhaut. 



5)T3 



C0NSTELLATI0N3 



SUMMARY. 
Stars of the I. II. _ UL , IV. V. _ VI. mag. 



Zodiacal 12 5 

North 34 6 

South 45 | _9_ 

Total.. 91 I 20 



646 1014 
635 1251 
323 363 



1604 3123 



Useful Works for the People. 




POPULAR LECTURES 




019 



ASTRONOMY : 



BY M. ARAGO. 



WITH ADDITIONS AND CORRECTIONS, 



BY DIONYSIUS LARDNER, LLB, 



THIRD EDITION 




NEW-YORK: 
GREELEY & McELRATH, TRIBUNE BUILDINGS, 

opposite the crry halil. 



1848. 




JPrice 25 Cents. 



■W*"WWV»,'*'W%-».-»fk-v«v^»k-S^« 



THE NEW-YORK TRIBUNE. 



We are on the -eve of another Presidential Election.— 
Let none fancy that, since it is approached so calmly, it 
will be conducted sluggishly and terminated without ex- 
citement. Whoever cherishes such an illusion mistakes 
the character of the American People and the impulses 
-which sway them. Equally idle is the imagination that 
Party lines are to be effaced and broken down in this con- 
test—that the prestige of some heroic achievement or the 
glitter of an epaulette is to chase from the popular mind 
ail memory of the radical differences of sentiment which 
have so often arrayed one-half our countrymen in fierce 
conflict with the other. Idle chimeras :these! offspring 
of an empty heart or a sickly brain ! With the progress- 
of events a particular measure may become more or less 
important, the emphatic assertion of a certain principle 
more or less essential, but the question of questions re- 
mains and will remain. At one time, the establishment 
or maintenance of a Sound and Uniform Currency ; at 
another, the upbuilding and cherishing of new or feeble 
branches of Home Industry ; at another, the proper dispo- 
sition of the Proceeds of the Public Lands; at a fourth, 
Peace or War, Spoliation or Justice ; but underneath all 
these, mightier than any, more enduring than all, lives ev- 
er the elemental difference in which parties have their 
origin— on one side the idea that Government should be 
Creative, Constructive, Beneficent ; on the other, the 
negative, skeptical, do-nothing element, whose axioms 
are ' The best Government is that which governs least,' 
' The People are inclined to expect too much from Gov- 
ernment,' &c— which sees in a Canal, a Railroad, a Har- 
bor, a Protective Duty, only a means of enriching a few 
individuals at the expense of the community, and which 
cannot conceive how any can be benefited by a public 
work without inflicting injury in at least equal measure 
upon others. The fundamental axioms of this negative 
philosophy are really hostile to Common Roads and Com- 
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those elements of National well-being against which it 
now directs the energies of a great party. The antag- 
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of the nature and true ends of Government cannot, in the 
nature of things.'be "lastingly compromised ; it cannot be 
terminated by the result of any one election. It must 
be potentially felt m the party contests and popular agi-. 
tations of many years to oome. 

On this and all the great questions growing out of it, 
The Tribune maintains emphatically the doctrines of the 
Whig Party. It advocates Protection to Home Indus- 
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extent of the necessity; a National Currency, sound 
and of uniform value, composed of Coin and Paper in 
'such proportions as public interest and general conven- 
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General and State Governments, each in its own sphere, 
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throughout all future time. Above all, this paper will 
1 study the things that make for Peace,' and strenuously 
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the passion for Military Glory, so mortally adverse to all 



the ideas of Social and Political Economy to which it is 
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variance with Christianity, and as a scandal to the Nine- 
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to the Extension of Human Slavery over one foot of soil 
where it has not now a legal existence shall be unsparing, 
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